Geometry Curriculum Map
Topic 1: Tools of Geometry
Big Idea 1: Visualization - Essential Question:
How can you represent a three-dimensional figure with a
two-dimensional drawing?
Big Idea 2: Reasoning - Essential Question:
What are the building blocks of Geometry?
Lesson Focus
Standard
Section
Critical Area
Domain
Cluster
1.1
Critical Area
1
Congruence (G.CO)
Experiment with
transformations in the plane
G.CO.1
1.2
Critical Area
1
Congruence (G.CO)
Experiment with
transformations in the plane
G.CO.1
Critical Area
1
Congruence (G.CO)
Experiment with
transformations in the plane
G.CO.1
Critical Area
4
Expressing Geo. Prop.
with Equations
(G.GPE)
Use coordinates to prove simple
geometric theorems algebraically
G.GPE.6
Critical Area
1
Congruence (G.CO)
Experiment with
transformations in the plane
G.CO.1
Congruence (G.CO)
Experiment with
transformations in the plane
G.CO.1
Congruence (G.CO)
Make geometric constructions
G.CO.12
Congruence (G.CO)
Experiment with
transformations in the plane
G.CO.1
Expressing Geo. Prop.
with Equations
(G.GPE)
Use coordinates to prove simple
geometric theorems algebraically
G.GPE.4
G.GPE.7
Critical Area
4
Expressing Geo. Prop.
with Equations
(G.GPE)
Use coordinates to prove simple
geometric theorems algebraically
G.GPE.6
Algebra 1
Critical Area
1
Quantities (N.Q)
Reason quantitatively and use
units to solve problems.
N.Q.1
1.3
1.4
1.5
1.6
1.7
1.8
1
Prepares for
Critical Area
1
Critical Area
1
Critical Area
1
Prepares for
Critical Area
4
Big Idea 3: Measurement - Essential Question:
How can you describe the attributes of a segment or
angle?
Enduring Understandings
(1) A three-dimensional object can be represented with a twodimensional figure using special drawing techniques such as nets,
isometric drawings and orthographic drawings.
(1) Geometry is a mathematical system built on accepted facts, basic
terms, and definitions. (2) A postulate or axiom is an accepted
statement of fact.
(1) Number operations can be used to find and compare the
lengths of segments. (2) The Ruler and Segment Addition
Postulates can be used in reasoning about lengths.
(1) Number operations can be used to find and compare the measure
of angles. (2) The Protractor and Angle Addition Postulates can be
used in reasoning about angle measures.
(1) Special angle pairs such as adjacent, vertical, complementary, and
supplementary angles can be used to identify geometric relationships
and to find angle measures.
(1) Special geometric tools can be used to make a figure
without measuring. (2) Construction with a straightedge and
compass is more accurate than sketching and drawing.
(1) Formulas can be used to find the midpoint and length of
any segment in the coordinate plane.
(1) Perimeter, circumference, and area are different ways of
measuring the size of geometric figures. (2) The area of a
region is the sum of the areas of its non-overlapping parts.
Pearson Geometry
Geometry Curriculum Map
Topic 2: Reasoning and Proof
Big Idea 1: Visualization - Essential Question:
How can you make a conjecture and prove that it is true?
Section
Critical Area
2.1
Prepares for
Critical Area
1
Congruence (G.CO)
Prove geometric theorems
2.2
Critical Area
1
Congruence (G.CO)
Prove geometric theorems
2.3
Critical Area
1
Congruence (G.CO)
Prove geometric theorems
2.4
Prepares for
Critical Area
1
Congruence (G.CO)
Prove geometric theorems
2.5
Prepares for
Critical Area
1
Congruence (G.CO)
Prove geometric theorems
G.CO.9
G.CO.10
G.CO.11
2.6
Critical Area
1
Congruence (G.CO)
Prove geometric theorems
G.CO.9
2
Domain
Cluster
Lesson Focus
Standard
G.CO.9
G.CO.10
G.CO.11
G.CO.9
G.CO.10
G.CO.11
G.CO.9
G.CO.10
G.CO.11
G.CO.9
G.CO.10
G.CO.11
Enduring Understandings
(1) Patterns in some number sequences and some sequences of
geometric figures can be used to discover relationships. (2)
Conjectures are not valid unless they are proven true. (3) One
counterexample can prove that a conjecture is false.
(1) Some mathematical relationships can be described using a
variety of if-then statements. (2) Each conditional statement
has a converse, an inverse, and a contra-positive.
(1) A definition is good if it can be written as a bi-conditional.
(2) Every bi-conditional can be written as two conditionals that
are converses of each other.
(1) Given true statements, deductive reasoning can be used to
make a valid or true conclusion. (2) Deductive reasoning often
involves the Laws of Syllogism and Detachment.
(1) Logical reasoning from one step to another is essential in
building a proof. (2) Reasons in a proof include given
information, definitions, properties, postulates and previously
proven theorems.
(1) Given information, definitions, properties, postulates and
previously proven theorems can be used as reasons in a proof.
Pearson Geometry
Geometry Curriculum Map
Topic 3: Parallel and Perpendicular Lines
Big Idea 1: Reasoning and Proof - Essential Question:
How do you prove that two lines are parallel or
perpendicular?
Section
3.1
3
Critical Area
Critical Area
1
Domain
Congruence (G.CO)
Big Idea 2: Measurement - Essential Question:
Big Idea 3: Coordinate Geometry - Essential
Question:
How do you write an equation of a line in a
coordinate plane?
What is the sum of the measures of the angles of
a triangle?
Lesson Focus
Cluster
Standard
Enduring Understandings
Experiment with
(1) Not all lines and not all planes intersect. (2) When a line
G.CO.1
transformations in the plane
intersects two or more lines, the angles forms at the
intersection points create special angle pairs.
Prove geometric theorems
G.CO.9
Prepares for
Critical Area 1
Congruence (G.CO)
3.2
Critical Area
1
Congruence (G.CO)
Prove geometric theorems
G.CO.9
3.3
Extends
Critical Area
1
Congruence (G.CO)
Prove geometric theorems
G.CO.9
3.4
Critical Area
2
Modeling with
Geometry (G.MG)
Apply geometric concepts in
modeling situations
G.MG.3
3.5
Critical Area
1
Congruence (G.CO)
Prove geometric theorems
G.CO.10
3.6
Critical Area
1
Congruence (G.CO)
Make geometric constructions
G.CO.12
G.CO.13
3.7
Prepares for
Critical Area
4
Expressing Geo.
Prop. with
Equations (G.GPE)
Use coordinates to prove simple
geometric theorems
algebraically
G.GPE.5
3.8
Critical Area
4
Expressing Geo.
Prop. with
Equations (G.GPE)
Use coordinates to prove simple
geometric theorems
algebraically
G.GPE.5
(1) The special angle pairs formed by parallel lines and a transversal
area either congruent or supplementary. Geometric postulates and
theorems can be combined with algebra to find angle measures.
(1) Certain angle pairs can be used to decide whether two
angles are parallel. (2) Paragraph, two-column, and flow
proofs are three forms of proof.
(1) The relationships of two lines to a third line can be used to
decide whether two lines are parallel or perpendicular to each
other.
(1) The sum of the angle measures of a triangle is always the
same. (2) Any exterior angle of a triangle has a special
relationship with the two remote interior angles of a triangle.
(1) Parallel and perpendicular lines can be constructed with a
straightedge and compass. (2) Special quadrilaterals can be
constructed with a straightedge and compass.
(1) A line can be graphed and its equation written when certain
facts about the line, such as its slope and a point on the line
are known. (2) The equation of a line can be written in various
forms.
(1) Comparing the slopes of two lines can show whether the
lines are parallel or perpendicular. (2) The relationship between
parallel or perpendicular can sometimes be used to write the
equation of a line.
Pearson Geometry
Geometry Curriculum Map
Topic 4: Congruent Triangles
Big Idea 1: Visualization - Essential Question:
How do you identify corresponding parts of congruent
triangles?
Big Idea 2: Reasoning and Proof - Essential
Question:
How do you show that two triangles are
congruent?
Lesson Focus
Cluster
Standard
Section
Critical Area
Domain
4.1
Prepares for
Critical Area
2
Similarity, Right
Triangles, &
Trigonometry (G.SRT)
4.2
Critical Area
2
Similarity, Right
Triangles, &
Trigonometry (G.SRT)
Prove theorems involving
similarity
G.SRT.5
4.3
Critical Area
2
Similarity, Right
Triangles, &
Trigonometry (G.SRT)
Prove theorems involving
similarity
G.SRT.5
Critical Area
2
Similarity, Right
Triangles, &
Trigonometry (G.SRT)
Prove theorems involving
similarity
G.SRT.5
Critical Area
1
Congruence (G.CO)
4.4
Critical Area
1
4.5
Critical Area
2
4
Congruence (G.CO)
Congruence (G.CO)
Similarity, Right
Triangles, &
Trigonometry (G.SRT)
Prove theorems involving
similarity
Make geometric
constructions
Prove geometric theorems
Make geometric
constructions
Prove theorems involving
similarity
G.SRT.5
Big Idea 3: Reasoning and Proof - Essential Question:
How can you tell whether a triangle is isosceles or
equilateral?
Enduring Understandings
(1) Comparing the corresponding parts of two figures can show
whether the figures are congruent.
(1) Two triangles can be proven to be congruent without
having to show that all corresponding parts are congruent. (2)
Two ways triangles can be proven to be congruent are by using
three pairs of corresponding sides or by using two pairs of
corresponding sides and one pair of corresponding angles.
(1) Two triangles can be proven to be congruent without
having to show that all corresponding parts are congruent. (2)
Another way triangles can be proven to be congruent is by
using one pair of corresponding sides and two pairs of
corresponding angles.
(1) If two triangles are congruent, then every pair of their
corresponding parts are also congruent.
G.CO.12
G.CO.10
G.CO.13
(1) The angles and sides of isosceles and equilateral triangles
have special relationships.
G.SRT.5
Pearson Geometry
Geometry Curriculum Map
Topic 4: Congruent Triangles (Continued)
Big Idea 1: Visualization - Essential Question:
Big Idea 2: Reasoning and Proof - Essential
Big Idea 3: Reasoning and Proof - Essential Question:
Question:
How do you identify corresponding parts of congruent
How do you show that two triangles are
How can you tell whether a triangle is isosceles or
triangles?
congruent?
equilateral?
Lesson Focus
Section Critical Area
Cluster
Standard
Enduring Understandings
Domain
(1) Two triangles can be proven to be congruent without
Similarity, Right
having to show that all corresponding parts are congruent. (2)
Critical Area
Triangles, &
Prove theorems involving
4.6
G.SRT.5
Another way triangles can be proven to be congruent is by
2
Trigonometry
similarity
using one pair of right angles, a pair of hypotensuses and a
(G.SRT)
pair of legs.
Similarity, Right
(1) Congruent corresponding parts of one pair of congruent
Critical Area
Triangles, &
Prove theorems involving
4.7
G.SRT.5
triangles can sometimes be used to prove another pair of
2
Trigonometry
similarity
triangles congruent. This often involves overlapping triangles.
(G.SRT)
5
Pearson Geometry
Geometry Curriculum Map
Topic 5: Relationships within Triangles
Big Idea 1: Coordinate Geometry - Essential Question:
How do you use coordinate geometry to find
relationships within triangles?
Section
5.1
5.2
5.3
5.4
Critical Area
Critical Area
1
Critical Area
2
Domain
Congruence (G.CO)
Congruence (G.CO)
Similarity, Right
Triangles, &
Trigonometry
(G.SRT)
Big Idea 2: Measurement - Essential Question: Big Idea 3: Reasoning and Proof - Essential Question:
How do you solve problems that involve
How do you write indirect proofs?
measurements of triangles?
Lesson Focus
Cluster
Standard
Enduring Understandings
Prove geometric theorems
G.CO.10
(1) To draw a mid-segment, students must find the midpoint of
Make geometric constructions
G.CO.12
two sides of a triangle and draw the segment joining the
midpoints. (2) The mid-segment of a triangle is related to the
Prove theorems involving
G.SRT.5
third side in two ways.
similarity
Critical Area
1
Congruence (G.CO)
Prove geometric theorems
G.CO.9
Critical Area
2
Similarity, Right
Triangles, &
Trigonometry
(G.SRT)
Prove theorems involving
similarity
G.SRT.5
Critical Area
5
Circles (G.C)
Understand and apply theorems
about circles
G.C.3
Critical Area
1
Congruence (G.CO)
Prove geometric theorems
G.CO.10
Critical Area
2
Similarity, Right
Triangles, &
Trigonometry
(G.SRT)
Prove theorems involving
similarity
G.SRT.5
(1) There is a special relationship between the points on the
perpendicular bisector of a segment and the endpoints of a
segment. (2) There is a special relationship between the points
on the bisector of an angle and the sides of an angle.
(1) A triangle’s three perpendicular angle bisectors are always
concurrent. (2) A triangle’s three angle bisectors are always
concurrent.
(1) A triangle’s three medians are always concurrent. (2) A
triangle’s three altitudes are always concurrent.
Topic 5: Relationships within Triangles (Continued)
6
Pearson Geometry
Geometry Curriculum Map
Big Idea 1: Coordinate Geometry - Essential Question:
How do you use coordinate geometry to find
relationships within triangles?
Section
Critical Area
Domain
5.5
Extends
Critical Area
1
Congruence (G.CO)
5.6
5.7
7
Extends
Critical Area
1
Extends
Critical Area
1
Congruence (G.CO)
Congruence (G.CO)
Big Idea 2: Measurement - Essential Question: Big Idea 3: Reasoning and Proof - Essential Question:
How do you solve problems that involve
How do you write indirect proofs?
measurements of triangles?
Lesson Focus
Cluster
Standard
Enduring Understandings
(1) In indirect reasoning, all possibilities are considered and
then all but one are proved false. The remaining possibility
Prove geometric theorems
G.CO.10
must be true. (2) An essential element of an indirect proof is
showing a contradiction.
(1) The measures of the angles of a triangle are related to the
Prove geometric theorems
G.CO.10
lengths of the opposite sides. The sum of the lengths of two
sides of a triangle is related to the length of the third side.
In triangles that have two pairs of congruent sides, there is a
Prove geometric theorems
G.CO.10
relationship between the included angles and the third pair of
sides.
Pearson Geometry
Geometry Curriculum Map
Topic 6: Polygons and Quadrilaterals
Big Idea 1: Measurement - Essential Question:
How can you find the sum of the measures of polygon
angles?
Big Idea 2: Reasoning and Proof - Essential
Question:
How can you classify quadrilaterals?
Lesson Focus
Standard
Section
Critical Area
Domain
Cluster
6.1
Critical Area 2
Similarity, Right
Triangles, &
Trigonometry (G.SRT)
Prove theorems involving
similarity
G.SRT.5
Prove geometric theorems
G.CO.11
Prove theorems involving
similarity
G.SRT.5
Prove geometric theorems
G.CO.11
Critical Area 1
6.2
Critical Area 2
Critical Area 1
6.3
6.4
6.5
6.6
8
Congruence (G.CO)
Similarity, Right
Triangles, &
Trigonometry (G.SRT)
Congruence (G.CO)
Critical Area 2
Similarity, Right
Triangles, &
Trigonometry (G.SRT)
Prove theorems involving
similarity
G.SRT.5
Critical Area 1
Congruence (G.CO)
Prove geometric theorems
G.CO.11
Critical Area 2
Similarity, Right
Triangles, &
Trigonometry (G.SRT)
Prove theorems involving
similarity
G.SRT.5
Critical Area 1
Congruence (G.CO)
Prove geometric theorems
G.CO.11
Critical Area 2
Similarity, Right
Triangles, &
Trigonometry (G.SRT)
Prove theorems involving
similarity
G.SRT.5
Critical Area 2
Similarity, Right
Triangles, &
Trigonometry (G.SRT)
Prove theorems involving
similarity
G.SRT.5
Big Idea 3: Coordinate Geometry - Essential
Question:
How can you use coordinate geometry to prove
general relationships?
Enduring Understandings
(1) The sum of the angle measures of a polygon depends on the
number of sides the polygon has.
(1) Parallelograms have special properties regarding their
sides, angles and diagonals. (2) Parallelograms can be used to
prove theorems about parallel lines and their transversals.
(1) If a quadrilateral’s sides, angles and diagonals have certain
properties, it can be shown that the quadrilateral is a
parallelogram. (2) The properties of parallelograms and
algebra can be used to find the lengths of some sides and the
measures of some angles of some parallelograms.
(1) The special parallelograms, rhombus, rectangle, and square
have basic properties about their sides, angles, and diagonals
that helped identify them.
(1) A parallelogram can be shown to be a rhombus, rectangle,
or square based on the properties of its diagonals.
(1) The angles, sides, and diagonals of a trapezoid have certain
properties.
Pearson Geometry
Geometry Curriculum Map
Topic 6: Polygons and Quadrilaterals
Big Idea 1: Measurement - Essential Question:
How can you find the sum of the measures of polygon
angles?
Big Idea 3: Coordinate Geometry - Essential
Question:
How can you use coordinate geometry to prove
general relationships?
Domain
Expressing Geo.
Prop. with
Equations (G.GPE)
Lesson Focus
Cluster
Standard
Use coordinates to prove simple
geometric theorems
G.GPE.7
algebraically
Critical Area
4
Expressing Geo.
Prop. with
Equations (G. GPE)
Use coordinates to prove simple
geometric theorems
algebraically
G.GPE.4
(1) Using variables to name the coordinates of a figure allows
relationships to be shown to be true for a general case.
Critical Area
4
Expressing Geo.
Prop. with
Equations (G. GPE)
Use coordinates to prove simple
geometric theorems
algebraically
G.GPE.4
(1) Geometric relationships can be proven using variable
coordinates for figures in the coordinate plane.
Section
Critical Area
6.7
Critical Area
4
6.8
6.9
9
Big Idea 2: Reasoning and Proof - Essential
Question:
How can you classify quadrilaterals?
Enduring Understandings
(1) The formulas for slope, distance, and midpoint can be used
to classify and prove geometric relationships for figures in the
coordinate plane .
Pearson Geometry
Geometry Curriculum Map
Topic 7: Similarity
Big Idea 1: Similarity - Essential Question:
How do you use proportions to find side lengths in similar
polygons?
Section
Critical Area
7.1
Critical Area
2
7.2
Critical Area
2
Critical Area
2
7.3
Critical Area
4
Critical Area
2
7.4
Critical Area
4
7.5
10
Critical Area
2
Domain
Similarity, Right
Triangles, &
Trigonometry
(G.SRT)
Similarity, Right
Triangles, &
Trigonometry
(G.SRT)
Similarity, Right
Triangles, &
Trigonometry
(G.SRT)
Expressing Geo.
Prop. with
Equations (G.GPE.5)
Similarity, Right
Triangles, &
Trigonometry
(G.SRT)
Expressing Geo.
Prop. with
Equations (G.GPE.5)
Similarity, Right
Triangles, &
Trigonometry
(G.SRT)
Big Idea 2: Reasoning and Proof - Essential
Question:
How do you show two triangles are similar?
Cluster
Lesson Focus
Standard
Prove theorems involving
similarity
G.SRT.5
Prove theorems involving
similarity
G.SRT.5
Prove theorems involving
similarity
G.SRT.5
Use coordinates to prove simple
geometric theorems
algebraically
G.GPE.6
Prove theorems involving
similarity
G.SRT.5
Use coordinates to prove simple
geometric theorems
algebraically
G.GPE.6
Prove theorems involving
similarity
G.SRT.4
Big Idea 3: Visualization - Essential Question:
How do you identify corresponding parts of similar
triangles?
Enduring Understandings
(1) A ratio can be written to compare two quantities. (2) an
equation can be written stating that two ratios are equal. (3) If
the equation contains a variable, it can be solved to find the
value of the variable.
(1) Ratios and proportions can be used to decide whether two
polygons are similar and to find the unknown side lengths of
similar figures. (2) All lengths in a scale drawing are
proportional to their corresponding actual lengths.
(1) Triangles can be shown to be similar based on the
relationship of two or three pairs of corresponding parts. (2)
Similar triangles can be used to find unknown measurements.
(1) Drawing in the altitude to the hypotenuse of a right triangle
forms three pairs of similar right triangles. (2) The altitude to
the hypotenuse of a right triangle, the segments formed by the
altitude, and the sides of the right triangles have lengths that
are related using geometric means.
(1) When two or more parallel lines intersect other lines,
proportional segments are formed. (2) The bisector of an angle
of a triangle divides the opposite side into two segments with
lengths proportional to the sides of the triangle that form the
angle
Pearson Geometry
Geometry Curriculum Map
Topic 8: Right Triangles and Trigonometry
Big Idea 1: Measurement - Essential Question:
How do you find a side length or angle measurement in a right triangle?
Section
8.1
8.2
8.3
Domain
Cluster
Critical Area
2
Similarity, Right
Triangles, &
Trigonometry
(G.SRT)
Define trigonometric ratios and
solve problems involving right
triangles
Critical Area
2
Critical Area
2
Critical Area
2
8.4
Critical Area
2)
8.5
Critical Area
2
Similarity, Right
Triangles, &
Trigonometry
(G.SRT)
8.6
Critical Area
2
Similarity, Right
Triangles, &
Trigonometry
(G.SRT)
11
Lesson Focus
Standard
Critical Area
Similarity, Right
Triangles, &
Trigonometry
(G.SRT)
Similarity, Right
Triangles, &
Trigonometry
(G.SRT)
Modeling with
Geometry (G.MG)
Similarity, Right
Triangles, &
Trigonometry
(G.SRT)
Big Idea 2: Similarity - Essential Question:
How do trigonometric ratios relate to similar right triangles?
G.SRT.8
Define trigonometric ratios and
solve problems involving right
triangles
G.SRT.8
Define trigonometric ratios and
solve problems involving right
triangles
G.SRT.8
G.SRT.7
Apply geometric concepts in
modeling situations
G.MG.1
Define trigonometric ratios and
solve problems involving right
triangles
G.SRT.8
Apply trigonometry to general
triangles
Apply trigonometry to general
triangles
G.SRT.11
G.SRT.10
G.SRT.11
G.SRT.10
Enduring Understandings
(1) If the lengths of any two sides of a right triangle are known,
the length of the third side can be found using the Pythagorean
Theorem. (2) If the lengths of all sides of a triangle are known,
it can be determined whether the triangle is acute, right, or
obtuse.
(1) Certain right triangles have properties that allow their side
lengths to be determined without using the Pythagorean
Theorem.
(1) If certain combinations of side lengths and angle measures
of a right triangle are known, ratios can be used to find other
side lengths and angle measures.
(1) The angles of elevation and depression are the acute angles
of right triangles formed by a horizontal distance and a vertical
height.
(1) If the measures of two angles and a side of a triangle are
known (AAS or ASA), or if the measures of two sides and a nonincluded angle are known (SSA), all the other measures of the
triangle can be found.
(1) If the measures of two sides lengths of a triangle and their
included angle (SAS) are known, or all three side lengths are
known (SSS), all the other measures of the triangle can be
found.
Pearson Geometry
Geometry Curriculum Map
Topic 9: Right Triangles and Trigonometry
Big Idea 1: Transformations - Essential Question:
Big Idea 2: Coordinate Geometry - Essential
Big Idea 3: Visualization - Essential
Question:
Question:
How can you change a figure's position without changing its size and
How can you represent a transformation in the
How do you recognize congruence
shape? How can you change a figure's size without changing its shape?
coordinate plane?
and similarity in figures?
Lesson Focus
Section Critical Area
Cluster
Standard
Enduring Understandings
Domain
(1)
The
location
and
orientation of a geometric figure can be
Critical Area
Experiment with
G.CO.1
Congruence (G.CO)
changed while preserving the distance and angle measures. (2)
1
transformations in the plane
G.CO.4
9.1
The distance between any two points, angle measures, and
Critical Area
Understand congruence in terms
orientation of a geometric figure remain the same when the
Congruence (G.CO)
G.CO.6
1
of rigid motions
figure is translated in one direction.
G.CO.2
Critical Area
Experiment with
Congruence (G.CO)
G.CO.4
(1) When you reflect a figure across a line, each point of the
1
transformations in the plane
G.CO.5
9.2
figure goes to another point the same distance from the line,
but on the other side.
Critical Area
Understand congruence in terms
Congruence (G.CO)
G.CO.6
1
of rigid motions
Critical Area
Experiment with
G.CO.2
Congruence (G.CO)
1
transformations in the plane
G.CO.4
(1) Distances, angle measures, and orientation of a geometric
9.3
figure is rotated about a center of rotation.
Critical Area
Understand congruence in terms
Congruence (G.CO)
G.CO.6
1
of rigid motions
Critical Area
Experiment with
Congruence (G.CO)
G.CO.5
(1) If there is an isometry that maps a figure to another, then
1
transformations in the plane
9.4
you can map one onto the other by using a composition of
Critical Area
Understand congruence in terms
reflections.
Congruence (G.CO)
G.CO.6
1
of rigid motions
G.CO.6
Critical Area
Understand congruence in terms
(1) If two figures can be mapped to each other by a sequence
9.5
Congruence (G.CO)
G.CO.7
1
of rigid motions
of rigid motions, then the figures are congruent.
G.CO.8
Similarity, Right
G.SRT.1a
Critical Area
Triangles, &
Apply trigonometry to general
(1) A scale factor can be used to make a larger or smaller copy
9.6
G.SRT.1b
1
Trigonometry
triangles
of a figure that is also similar to the original figure.
G.SRT.2
(G.SRT)
12
Pearson Geometry
Geometry Curriculum Map
Topic 9: Right Triangles and Trigonometry
Big Idea 1: Transformations - Essential Question:
Big Idea 2: Coordinate Geometry - Essential
Big Idea 3: Visualization - Essential
Question:
Question:
How can you change a figure's position without changing its size and
How can you represent a transformation in the
How do you recognize congruence
shape? How can you change a figure's size without changing its shape?
coordinate plane?
and similarity in figures?
Lesson Focus
Section Critical Area
Cluster
Standard
Enduring Understandings
Domain
Similarity, Right
(1) Compositions of rigid motions and dilations can be used to
Critical Area
Triangles, &
Apply trigonometry to general
G.SRT.2
understand the properties of similarity. (2) Two figures are
9.7
1
Trigonometry
triangles
G.SRT.3
similar if there is a similarity transformation that maps one
(G.SRT)
onto the other.
13
Pearson Geometry
Geometry Curriculum Map
Topic 10: Area
Big Idea 1: Measurement - Essential Question:
Big Idea 2: Similarity - Essential Question:
How do you find the area of a polygon or find the circumference and area of a
How do perimeters and areas of similar polygons compare?
circle?
Lesson Focus
Section Critical Area
Cluster
Standard
Enduring Understandings
Domain
Critical Area
Modeling with
Apply geometric concepts in
G.MG.1
3
Geometry (G.MG)
modeling situations
(1) The area of a parallelogram or a triangle can be found
10.1
Expressing Geo.
Use coordinates to prove simple
when the length of its base and its height are known.
Critical Area
Prop. with
geometric theorems
G.GPE.7
4
Equations (G. GPE)
algebraically
(1) The area of a trapezoid can be found when the lengths of its
Critical Area
Modeling with
Apply geometric concepts in
10.2
G.MG.1
base and its height are known. (2) The area of a rhombus or
3
Geometry (G.MG)
modeling situations
kite can be found when the lengths of its diagonals are known.
Critical Area
Modeling with
Apply geometric concepts in
G.MG.1
3
Geometry (G.MG)
modeling situations
(1) The area of a regular polygon is a function of the distance
10.3
from the center to a side and the perimeter.
Critical Area
Congruence (G.CO)
Make geometric constructions
G.CO.13
1
10.4
10.5
10.6
14
Prepares for
Critical Area
3
Geometric
Measurement &
Dimension (G.SRT)
Critical Area
2
Similarity, Right
Triangles, &
Trigonometry
(G.SRT)
Apply trigonometry to general
triangles
G.SRT.9
Critical Area
1
Congruence (G.CO)
Experiment with
transformations in the plane
G.CO.1
Critical Area
5
Critical Area
5
Circles (G.C)
Circles (G.C)
Explain volume formulas and use
them to solve problems
Understand and apply theorems
about circles
Find arc lengths and areas of
sectors of circles
G.GMD.3
G.C.1
G.C.2
(1) Ratios can be used to compare the perimeters and areas of
similar figures.
(1) Trigonometry can be used to find the area of a regular
polygon when the length of a side, radius, or apothem is
known. (2) Trigonometry can be used to find the area of a
triangle when the lengths of two side and the included angle
are known .
(1) The length of part of a circle's circumference can be found
by relating it to a central angle of the circle.
G.C.5
Pearson Geometry
Geometry Curriculum Map
Topic 10: Area (Continued)
Big Idea 1: Measurement - Essential Question:
Big Idea 2: Similarity - Essential Question:
How do you find the area of a polygon or find the circumference and area of a
How do perimeters and areas of similar polygons compare?
circle?
Lesson Focus
Section Critical Area
Cluster
Standard
Enduring Understandings
Domain
(1) The area of a circle can be found when the circle's radius is
Critical Area
Find arc lengths and areas of
known. (2) The area of parts of a circle formed by the radii and
10.7
Circles (G.C)
G.C.5
5
sectors of circles
an arc can be found when the circle's radius and the arc
measure are known.
Conditional
Prepares for
Understand independence and
Probability & the
(1) Certain problems in probability can be solved by modeling
10.8
Critical Area
conditional probability and use
S.CP.1
Rules of Probability
the situation with geometric measures.
6
them to interpret data
(S.CP)
15
Pearson Geometry
Geometry Curriculum Map
Topic 11: Surface Area and Volume
Big Idea 1: Visualization - Essential Question:
How can you determine the intersection of a solid and a
plane?
Big Idea 2: Measurement - Essential Question:
How do you find the surface area and volume of a
solid?
Lesson Focus
Cluster
Standard
Big Idea 3: Similarity - Essential Question:
How do the surface areas and volumes of
similar solids compare?
Section
Critical Area
Domain
11.1
Critical Area
3
Geometric
Measurement &
Dimension (G.GMD)
Experiment with
transformations in the plane
G.GMD.4
(1) A three-dimensional figure can be analyzed by describing
the relationships between its vertices, edges and faces. (2) A
cross-section is the intersection of a three-dimensional figure
and a plane.
11.2
Critical Area
3
Modeling with
Geometry (G.MG)
Apply geometric concepts in
modeling situations
G.MG.1
(1) The area of a three-dimensional figure is equal to the sum
of the areas of each surface of the figure.
11.3
Critical Area
3
Modeling with
Geometry (G.MG)
Apply geometric concepts in
modeling situations
G.MG.1
1) The area of a three-dimensional figure is equal to the sum of
the areas of each surface of the figure.
Critical Area
3
Geometric
Measurement &
Dimension (G.GMD)
Explain volume formulas and use
them to solve problems
G.GMD.1
G.GMD.2
G.GMD.3
Critical Area
3
Modeling with
Geometry (G.MG)
Apply geometric concepts in
modeling situations
G.MG.1
11.4
16
Enduring Understandings
(1) The volume of a prism and a cylinder can be found when its
height and the area of the base are known. (2) The volume of a
composite space figure is the sum of the volumes of the figures
that are combined.
Pearson Geometry
Geometry Curriculum Map
Topic 11: Surface Area and Volume (Continued)
Big Idea 1: Visualization - Essential Question:
How can you determine the intersection of a solid and a
plane?
Section
11.5
Critical Area
Critical Area
3
Critical Area
3
11.6
11.7
17
Critical Area
3
Critical Area
3
Critical Area
2
Domain
Geometric
Measurement &
Dimension (G.GMD)
Modeling with
Geometry (G.MG)
Geometric
Measurement &
Dimension (G.GMD)
Modeling with
Geometry (G.MG)
Modeling with
Geometry (G.MG)
Big Idea 2: Measurement - Essential Question:
How do you find the surface area and volume of a
solid?
Lesson Focus
Cluster
Standard
Explain volume formulas and use
them to solve problems
G.GMD.3
Apply geometric concepts in
modeling situations
G.MG.1
Explain volume formulas and use
them to solve problems
G.GMD.3
Apply geometric concepts in
modeling situations
Apply geometric concepts in
modeling situations
Big Idea 3: Similarity - Essential Question:
How do the surface areas and volumes of
similar solids compare?
Enduring Understandings
(1) The volume of a pyramid is related to the volume of a prism
with the same base and height. (2) The volume of a cone is
related to the volume of a cylinder with the same base and
height.
(1) The surface area and the volume of a sphere can be found
when its radius is known.
G.MG.1
G.MG.1
G.MG.2
(1) Ratios can be used to compare the areas and volumes of
similar solids.
Pearson Geometry
Geometry Curriculum Map
Topic 12: Circles
Big Idea 1: Reasoning and Proof - Essential Question:
How can you prove relationships between angles and
arcs in a circle?
Section
Critical Area
12.1
Critical Area
5
12.2
Critical Area
5
Domain
Big Idea 2: Measurement - Essential Question:
When lines intersect a circle or within a circle, how do you
find the measures of resulting angles, arcs, and segments?
Lesson Focus
Cluster
Standard
Enduring Understandings
Circles (G.C)
Understand and apply theorems
about circles
Circles (G.C)
Understand and apply theorems
about circles
G.C.2
12.3
Critical Area
5
Circles (G.C)
Understand and apply theorems
about circles
G.C.2
G.C.3
G.C.4
12.4
Critical Area
5
Circles (G.C)
Understand and apply theorems
about circles
G.C.2
12.5
Critical Area
5
12.6
Critical Area
3
Expressing Geo.
Prop. with
Equations (G.GPE)
Geometric
Measurement &
Dimension (G.SRT)
Translate between the
geometric description and the
equation for a conic section
Visualize relationships between
two-dimensional and threedimensional objects
18
Big Idea 3: Coordinate Geometry Essential Question:
How do you find the equation of a circle in a
coordinate plane?
G.C.2
G.GPE.1
G.GMD.4
(1) A radius of a circle and the tangent that intersects the
endpoint of the radius on the circle have a special relationship.
(2) A circle has a special relationship to a triangle whose sides
are tangent to the circle.
(1) Information about congruent parts of a circle (or congruent
circles) can be used to find information about other parts of the
circle (or circles).
(1) Angles formed by intersecting lines have a special
relationship to the arcs the intersecting lines intercept. (2)
Specifically, arcs intercepted by chords that form inscribed
angles are related to the inscribed angles.
(1) Angles formed by intersecting lines have a special
relationship to the arcs the intersecting lines intercept. (2) Arcs
formed by lines intersecting either within a circle or outside a
circle are related to the angles formed by the lines. (3) There
are special relationships between intersecting chords,
intersecting secants, or a secant and tangent that intersect.
(1) The information in the equation of a circle allows the circle
to be graphed. (2) The equation of a circle can be written if its
center and radius are known.
(1) The description of a locus can be used to sketch a geometric
relationship.
Pearson Geometry
Geometry Curriculum Map
Topic 13: Probability
Big Idea 1: Probability - Essential Question:
What is the difference between experimental
probability and theoretical probability?
Section
Critical Area
13.1
Critical Area
6
13.2
Critical Area
6
13.3
Critical Area
6
13.4
Critical Area
6
13.5
Critical Area
6
Critical Area
6
13.6
Critical Area
6
19
Domain
Conditional
Probability & the
Rules of Probability
(S.CP)
Conditional
Probability & the
Rules of Probability
(S.CP)
Conditional
Probability & the
Rules of Probability
(S.CP)
Conditional
Probability & the
Rules of Probability
(S.CP)
Conditional
Probability & the
Rules of Probability
(S.CP)
Conditional
Probability & the
Rules of Probability
(S.CP)
Conditional
Probability & the
Rules of Probability
(S.CP)
Big Idea 2: Data Representation - Essential Question:
What is a frequency table?
Cluster
Lesson Focus
Standard
Big Idea 3: Probability - Essential Question:
What does it mean for an event to be
random?
Enduring Understandings
Understand independence and
conditional probability and use
them to interpret data
S.CP.1
S.CP.4
(1) Probability is the measure of the likelihood that an event
will occur .
Understand independence and
conditional probability and use
them to interpret data
S.CP.4
S.CP.5
(1) Tables can be used to organize data by frequency and find
probabilities.
S.CP.9
(1) Counting techniques can be used to find all of the possible
ways to complete different tasks or choose items from a list.
S.CP.7
S.CP.8
S.CP.9
(1) The probability of compound events can be found using the
probability of each part of the compound event..
Understand independence and
conditional probability and use
them to interpret data
S.CP.4
(1) Two-way frequency tables can be used to organize data,
identify sample spaces and approximate probabilities. (2) In
real-world situations, frequency tables can be used to find
conditional probabilities and determine if treatments are
effective.
Understand independence and
conditional probability and use
them to interpret data
S.CP.2
S.CP.3
S.CP.5
Use the rules of probability to
compute probabilities of
compound events in a uniform
probability model
S.CP.6
Use the rules of probability to
compute probabilities of
compound events in a uniform
probability model
Use the rules of probability to
compute probabilities of
compound events in a uniform
probability model
(1) Tables, tree diagrams, and formulas can be used to find
conditional probability.
Pearson Geometry
Geometry Curriculum Map
Topic 13: Probability (Continued)
Big Idea 1: Probability - Essential Question:
What is the difference between experimental
probability and theoretical probability?
Section
Critical Area
13.7
Critical Area
6
20
Domain
Using Probability to
Make Decisions
(S.MD)
Big Idea 2: Data Representation - Essential Question:
What is a frequency table?
Cluster
Lesson Focus
Standard
Calculate expected values and
use them to solve problems
S.MD.6
S.MD.7
Big Idea 3: Probability - Essential Question:
What does it mean for an event to be
random?
Enduring Understandings
(1) Probability and random selection can be used in making
appropriate and fair decisions .
Pearson Geometry