PACING GUIDES FOR MATH
Big Idea: Geometry
Prepared by Union County Schools
Grade Level: Tenth
Time Frame:
14 Days
14 Days
22 Days
10 Days
Unit Topic
(Specify
skills/information
that will be
learned.)
Enduring
Understandings
(Give and/or
demonstrate
necessary
information)
Unit 1
Reasoning and Proof
Unit 2
Spatial Visual
Unit 3
Triangles
Unit 4
2-Dimensional
In proofs, deductive
reasoning about given
information is used to
reach mathematical
conclusions.
Theorems and properties
exist that guarantee two
triangles are congruent or
similar given certain
conditions.
Relationships between
lines, angles and figures
can be used to establish
additional mathematical
relationships.
Congruent figures are also
similar figures, but similar
figures are not always
congruent.
Geometric figures and
relationships can be
represented in the
coordinate plane.
Geometric figures can
be measured in the
coordinate plane.
The slope of a line is the
ratio of vertical change
(rise) to horizontal
change (run).
Slopes, distances and
midpoints can be
determined when a
segment is graphed in
the coordinate plane.
A line’s direction and
steepness are
determined by its slope.
Linear equations can be
used to make
predictions.
The Pythagorean
Theorem is essential to
solving problems
involving right triangles.
Congruent figures are
also similar figures, but
similar figures are not
always congruent.
Congruency and
similarity have real life
applications in art,
architecture, and
science.
Parallel and
perpendicular lines are
used to prove triangles
congruent or similar.
30º-60º-90º and 45º45º-90º triangles are
similar triangles.
Polygons are categorized
by the number of sides.
Studying patterns can
lead to geometric
formulas and
relationships.
Rectangles, squares, and
rhombi are
parallelograms and
belong to the set of
quadrilaterals.
Relationships exist
between sides, angles
and segments in
polygons.
By using the area
formula of a rectangle,
we can derive area
formulas for other
figures.
PACING GUIDES FOR MATH
Big Idea: Geometry
Prepared by Union County Schools
Grade Level: Tenth
Time Frame:
14 Days
14 Days
22Days
10 Days
Enduring
Understandings
con’t
Parallel and perpendicular
lines are used to prove
triangles congruent or
similar.
A line’s slope and x- and
y-intercepts have real
world applications.
Special triangles have
real world applications.
Relationships in special
right triangles can be
determined by the
Pythagorean Theorem.
Essential
Questions
(Steps to check for
student
understanding)
Why write formal proofs?
Why are properties and
theorems about parallel
and perpendicular lines
useful in geometric proofs?
How can reasoning about
geometric situations be
used to solve real life
problems?
If two figures are
congruent or similar, what
else do you know about
their corresponding parts?
What theorems or
postulates (properties)
guarantee two triangles
congruent?
Why is it important to
learn about geometric
figures and relationships
in the coordinate plane?
How do you determine
information about a line
or segment graphed in
the coordinate plane?
How does the Distance
Formula relate to the
Pythagorean Theorem?
How do you represent
geometric figures in the
coordinate plane?
How do you measure
geometric figures using
the coordinate plane?
Why is the intersection
point of special segments
in triangles important?
What theorems
guarantee two triangles
congruent?
How do congruent
figures differ from
similar figures?
Where are parallel and
perpendicular lines
evident in everyday life?
How are the angles
formed by parallel lines
used to prove triangles
congruent?
Perimeter and
circumference are 1dimensional measures,
while area is a 2dimenionsal measure.
Measurement of
geometric figures is an
essential part everyday
life.
How can you use
patterns to find the sum
of the interior angles of
any polygon?
How can you determine
the measure of interior
and exterior angles in
regular polygons?
How do you classify
quadrilaterals using
special segments and
properties?
How do special
segments in polygons
help solve everyday
situations?
PACING GUIDES FOR MATH
Big Idea: Geometry
Prepared by Union County Schools
Grade Level: Tenth
Time Frame:
14 Days
14 Days
22 Days
10 Days
Essential
Questions
How do congruent figures
differ from similar figures?
How does slope describe
a line? How can you use
an equation to make a
prediction?
What does the slope of
the line tell you?
How do you write an
equation for a line?
How do you write an
equation for a line if you
are given two points?
How do you determine
the x- and y-intercepts
graphically and
algebraically?
How are properties of
perpendicular lines used
to prove congruent and
similar triangles?
How is the Pythagorean
Theorem related to the
lengths of sides of
special right triangles?
How does the concept of
similarity apply to
special right
triangles?How are right
triangle relationships
used in the real world?
How do you find the
lengths of sides of
special right triangles?
How can you derive the
various area formulas
from the area of a
rectangle?
How can you find the
areas of irregular
figures?
How does finding the
area of the various
figures apply to everyday
situations?How are
perimeter,
circumference, and area
different from one
another?
G-1.1 Demonstrate an
understanding of the
axiomatic structure of
geometry
using undefined terms,
definitions, postulates,
theorems, and corollaries.
G-2.4 Use direct
measurement to
determine the length of a
segment, measure
of an angle, and distance
from a point to a line.
G-6.1 Use the distance
formula to solve
problems.
G-3.1 Carry out a
procedure to compute
the perimeter of a
triangle.
G-3.2 Carry out a
procedure to compute
the area of a triangle.
G-3.3 Analyze how
changes in dimensions
affect the perimeter or
area of triangles.
G-2.3 Use the
congruence of line
segments and angles to
solve problems.
G-4.6 Apply congruence
and similarity between
shapes (including
quadrilaterals and
polygons) to solve
problems.
Standards
con’t
PACING GUIDES FOR MATH
Big Idea: Geometry
Prepared by Union County Schools
Grade Level: Tenth
Time Frame:
14 Days
14 Days
22 Days
10 Days
Standards con’t
G-1.2 Communicate
knowledge of geometric
relationships using
mathematical
terminology appropriately.
G-1.7 Understand the
historical development of
geometry.
G-1.4 Formulate and test
conjectures using a variety
of tools such as concrete
models, graphing.
calculators, spreadsheets,
and dynamic geometry
Software
G-1.9 Demonstrate an
understanding of how
geometry applies to real
world contexts (including
architecture, construction,
farming, astronomy).
G-6.2 Use the midpoint
formula to solve
problems.
G-2.2 Apply properties of
parallel lines,
intersecting lines, and
parallel lines cut
by a transversal to solve
problems.
G-2.5 Carry out a
procedure to create
geometric constructions
(including
midpoint of a line
segment, angle bisector,
perpendicular bisector of
a line segment, line
through a given point
that is parallel to a given
line,
and line through a given
point that is
perpendicular to a given
line).
G-3.4 Apply properties of
isosceles and equilateral
triangles to solve
problems.
G-3.5 Use interior
angles, exterior angles,
medians, angle bisectors,
altitudes,
and perpendicular
bisectors to solve
problems.
G-3.6 Apply the Triangle
Sum Theorem to solve
problems.
G-3.7 Apply the Triangle
Inequality Theorem to
solve problems.
G-3.8 Apply congruence
and similarity between
triangles to solve
problems.
G-3.9 Apply theorems to
prove triangles are
similar or congruent.
G-3.10 Use the
Pythagorean Theorem
and its converse to solve
problems.
G-2.5 Carry out a
procedure to create
geometric constructions
(including
midpoint of a line
segment, angle bisector,
perpendicular bisector of
a line segment, line
through a given point
that is parallel to a given
line,
and line through a given
point that is
perpendicular to a given
line).
G-4.6 Apply congruence
and similarity between
shapes (including
quadrilaterals and
polygons) to solve
problems.
G-2.6 Use scale factors
to solve problems
involving scale drawings
and
models.
PACING GUIDES FOR MATH
Big Idea: Geometry
Prepared by Union County Schools
Grade Level: Tenth
Time Frame:
14 Days
Standards
con’t
G-1.10 Understand
geometric relationships
including constructions
through investigations
using a variety of tools
such as straightedge,
compass,
paper folding, dynamic
geometry software, and
hand-held computing
devices.
G-1.3 Apply basic rules of
logic to determine the
validity of the converse,
inverse, and contrapositive
of a conditional statement
G-1.5 Use inductive
reasoning to formulate
conjectures.
G-1.6 Use deductive
reasoning to validate
conjectures with formal
and informal proofs, and
give counterexamples to
disprove a statement.
14 Days
22 Days
10 Days
G-3.11 Use the
properties of 45-45-90
and 30-60-90 triangles
to solve problems.
G-3.12 Use trigonometric
ratios (including sine,
cosine, tangent) to solve
problems involving right
triangles.
G-2.7 Use geometric
probability to solve
problems.
G-4.1 Carry out a
procedure to compute
the perimeter of
quadrilaterals,
regular polygons, and
composite figures.
G-4.2 Carry out a
procedure to find the
area of quadrilaterals,
regular polygons, and
composite figures.
G-4.3 Apply procedures
to compute measures of
interior and exterior
angles of polygons. area
of quadrilaterals and
regular polygons.
G-4.4 Analyze how
changes in dimensions
affect the perimeter or
area of quadrilaterals
and regular polygons
PACING GUIDES FOR MATH
Big Idea: Geometry
Prepared by Union County Schools
Grade Level: Tenth
Time Frame:
14 Days
14 Days
22 Days
Standards
con’t
Integrations
(with other
discipline areas)
District
Assessments
(culminating
assessments)
Benchmark Exam
10 Days
G-4.5 Apply
properties and
attributes of
quadrilaterals and
regular polygons
and their component
parts to solve
problems.
G-2.1 Infer missing
elements of visual or
numerical geometric
patterns (including
triangular numbers,
rectangular
numbers, and
number of diagonals
in polygons).
G-2.7 Use geometric
probability to solve
problems.
PACING GUIDES FOR MATH
Big Idea: Geometry
Prepared by Union County Schools
Grade Level: Tenth
Time Frame:
12 Days
5 Days
13 Days
Unit Topic
(Specify
skills/information
that will be
learned.)
Unit 5
3-Dimensional
Unit 6
Transformations
Unit 7
Circles
Enduring
Understandings
(Give and/or
demonstrate
necessary
information)
Three-dimensional
figures have properties
similar to those of twodimensional figures.
Transformations move or
map figures (preimages)
onto their images.
Reflections, rotations,
and translations are
transformations that
preserve shape and size
(congruency).
Dilation is a
transformation that
preserves shape only
(similarity).
Indirect measurement is
based on the properties
of geometric figures.
Relationships exist
among angles, segments,
lengths, circumference,
and area of circles.
Essential
Questions
(Steps to check
for student
understanding)
How are two-dimensional
relationships connected
to the properties of threedimensional figures?
Why do certain
transformations preserve
shape and size while
others only preserve
shape?
How does combining
transformations affect
the final result?
How are the coordinates
affected by
transformations in the
How are the areas of
polygons and circles
related and applied?
How are angles and
intercepted arcs of circles
related and applied?
PACING GUIDES FOR MATH
Big Idea: Geometry
Prepared by Union County Schools
Grade Level: Tenth
Time Frame:
12 Days
Essential
Questions
13 Days
coordinate plane?
How are scale factors
used in transformations?
con’t
Standards
5 Days
G-7.1 Carry out a
procedure to compute
the surface area of threedimensional
objects (including cones,
cylinders, pyramids,
prisms, spheres, and
hemispheres).
G-7.2 Carry out a
procedure to compute
the volume of threedimensional
objects (including cones,
cylinders, pyramids,
prisms, spheres,
hemispheres, and
composite objects).
G-7.3 Analyze how
changes in dimensions
affect the volume of
objects (including
cylinders, prisms, and
spheres).
G-6.3 Apply
transformations
(translation, reflection,
rotation, and dilation) to
figures in the coordinate
plane using sketches and
coordinates.
G-6.4 Apply
transformations
(including translation
and dilation) to figures in
the coordinate plane
using matrices.
G-6.5 Carry out a
procedure to represent
the sum of two vectors
geometrically by using
the parallelogram
method.
G-6.6 Carry out a
procedure to determine
the magnitude and
direction of the
resultant by direct
measurement using a
G-5.1 Carry out a
procedure to compute
the circumference of
circles.
G-5.2 Carry out a
procedure to compute
the area of circles.
G-5.3 Analyze how a
change in radius affects
the circumference or area
of a circle.
G-5.4 Carry out a
procedure to compute arc
length or area of a sector
of a circle.
G-5.5 Apply properties of
component parts of a
circle (including radii,
diameters, chords,
sectors, arcs, and
segments) to solve
problems.
Grade Level: Tenth
Time Frame:
Standards
PACING GUIDES FOR MATH
Big Idea: Geometry
Prepared by Union County Schools
12 Days
G-7.4 Apply
congruence and
similarity between
objects to solve
problems.
G-7.5 Apply a
procedure to draw a
top-view, front-view,
and side-view of a
three-dimensional
object.
G-7.6 Apply a
procedure to draw
an isometric view of
a three-dimensional
object
5 Days
scale drawing.
G-6.7 Carry out a
procedure to
compute the
magnitude of the
resultant of two
perpendicular
vectors using the
Pythagorean
Theorem.
G-6.8 Carry out a
procedure to
determine the
direction of the
resultant of two
perpendicular
vectors using direct
measurement.
13 Days
G-5.6 Apply
properties of lines
that intersect
circles(including two
secants, two
tangents, or a secant
and a tangent) to
solve problems.
G-5.7 Apply
properties of central
angles, inscribed
angles, and arcs of
circles to solve
problems.
G-2.7 Use geometric
probability to solve
problems.
Integrations
(with other
discipline areas)
District
Assessments
(culminating
assessments)
Final Exam