Year-at-a-Glance
MUHSD Geometry Pacing Guide
Dates
st
1
Quarter
10 days
15 days
15 days
5 days
McDougal Littell Units
Unit 1: Essentials of Geometry
Unit 2: Reasoning & Proof
Unit 3: Parallel & Perpendicular Lines
Unit 4: Congruent Triangles
Standards
1, 8, 10, 12
1, 2, 3
7
4, 5, 12, 13, 16
Quarter 1 Benchmark
2nd
Quarter
5 days
10 days
10 days
10 days
Unit 4: Congruent Triangles (Continued)
Unit 5: Relationships within Triangles
Unit 6: Similarity
Unit 7: Right Triangles & Trigonometry
4, 5, 12, 13, 16
2, 6, 12, 15, 17
4, 5, 7, 8, 11, 12
4, 12, 14, 15, 18, 19, 20
Semester 1 Final
3rd
Quarter
10 days
15 days
10 days
Unit 8: Quadrilaterals
Unit 10: Properties of Circles
Unit 11: Measuring Length & Area
7, 12
7, 17, 21
8, 10, 11
Quarter 3 Benchmark
4th
Quarter
15 days
5 days
5 days
Unit 12: Surface Area & Volume of Solids
Unit 9: Properties of Transformations
Unit 13: Constructions
8, 9, 11
5, 22
16
Semester 2 Final
* Preparation for Geometry Standard
1 of 6
Updated 7/29/2008
MUHSD Geometry Pacing Guide: 2008-2009 / 1st Quarter
Dates
Essential Standard Cluster
McDougal Littell Sections
1.0 – Students demonstrate understanding by
identifying and giving examples of undefined terms,
axioms, theorems, and inductive and deductive
reasoning.
10
days
8.0 – Students know, derive, and solve problems
involving the perimeter, circumference, area, volume,
lateral area, and surface area of common geometric
shapes.
Standard
Resources
Unit 1: ESSENTIALS OF GEOMETRY
1.1 - Identify points, lines and planes.
1.2 – Use segments and congruence
1.3* – Use midpoint and distance formulas
1.4 – Measure and classify angles
1.5 – Describe angle pair relationships
1.6* – Classify polygons
1.7 – Find perimeter, circumference, and area
1.0
1.0
Prepare for 17.0
1.0
12.0
Prepare for 13.0
8.0, 10.0
Unit 2: REASONING AND PROOF
2.1 – Use inductive reasoning
2.2 - Analyze conditional statements
2.3 - Apply deductive reasoning
2.4 – Use postulates and diagrams
2.5* – Reason using properties of algebra
2.6 – Prove statements about segments and Angles
2.7 – Prove angle pair relationships
1.0, 3.0
3.0
1.0, 3.0
1.0
1.0, 3.0
1.0, 2.0
1.0, 2.0, Prepare for 13.0
Unit 3: PARALLEL & PERPENDICULAR LINES
3.1 – Identify pairs of lines and angles
3.2 – Use parallel lines and transversals
3.3 – Prove lines are parallel
3.4 *– Find and use slopes of lines
3.5 *– Write and graph equations of lines
3.6 - Prove theorems about perpendicular lines
16.0, Prepare for 7.0
7.0
2.0, 7.0
Prepare for 17.0
Prepare for 17.0
7.0
10.0 – Students compute areas of polygons, including
rectangles, scalene triangles, equilateral triangles,
rhombi, parallelograms, and trapezoids.
12.0 – Students find and use measures of sides and of
interior and exterior angles of triangles and polygons
to classify figures and solve problems.
1.0 – Students demonstrate understanding by
identifying and giving examples of undefined
terms, axioms, theorems, and inductive and
deductive reasoning.
15
days
2.0 – Students write geometric proofs, including
proofs by contradiction.
3.0 – Students construct and judge the validity of a
logical argument and give counterexamples to
disprove a statement.
2.0 – Students write geometric proofs, including
proofs by contradiction.
15
days
7.0 – Students prove and use theorems involving the
properties of parallel lines cut by a transversal, the
properties of quadrilaterals, and the properties of
circles.
QUARTER 1 BENCHMARK
* Preparation for Geometry Standard
2 of 6
Updated 7/29/2008
MUHSD Geometry Pacing Guide: 2008-2009 / 2nd Quarter
Dates
Essential Standard Cluster
4.0 – Students prove basic theorems involving
congruence and similarity.
5.0 – Students prove that triangles are congruent or
similar, and they are able to use the concept of
corresponding parts of congruent triangles.
12.0 – Students find and use measures of sides and of
interior and exterior angles of triangles and polygons
to classify figures and solve problems.
2.0 – Students write geometric proofs, including
proofs by contradiction.
6.0 – Students know and are able to use the triangle
inequality theorem.
12.0 – Students find and use measures of sides and of
interior and exterior angles of triangles and polygons
to classify figures and solve problems.
McDougal Littell Sections
Standard
Resources
Unit 4: CONGRUENT TRIANGLES
4.1 – Apply triangle sum properties
4.2 – Apply congruence and triangles
4.3 – Prove triangles congruent by SSS
4.4 – Prove triangles congruent by SAS & HL
4.5 – Prove triangles congruent by ASA & AAS
4.6 – Use congruent triangles
4.7 – Use isosceles and equilateral triangles
4.8 – Perform congruence transformations
(Moved to Ch. 9)
12.0, 13.0
5.0
5.0, 16.0
4.0, 5.0
4.0, 5.0
5.0, 16.0
5.0, 12.0
22.0
Unit 5: RELATIONSHIPS WITHIN TRIANGLES
5.1 – Midsegment theorem and coordinate proof
5.2 – Use perpendicular bisectors
5.3 – Use angle bisectors of triangles
5.4 – Use medians and altitudes
5.5 – Use inequalities in a triangle
5.6 – Inequalities in 2 triangles & indirect proofs
17.0
12.0
12.0, 15.0
17.0, Prepare for 12.0
6.0, 12.0
2.0
17.0 – Students prove theorems by using coordinate
geometry, including the midpoint of a line segment,
the distance formula, and various forms of equations
of lines and circles.
* Preparation for Geometry Standard
3 of 6
Updated 7/29/2008
4.0 – Students prove basic theorems involving
congruence & similarity.
5.0 – Students prove that triangles are congruent or
similar, and they are able to use the concept of
corresponding parts of congruent triangles.
12.0 – Students find and use measures of sides and of
interior and exterior angles of triangles and polygons
to classify figures
4.0 – Students prove basic theorems involving
congruence & similarity.
14.0 – Students prove the Pythagorean Theorem.
15.0 – Students use the Pythagorean Theorem to
determine distance and find missing lengths of sides
of right triangles.
18.0 – Students know the definitions of the basic
trigonometric functions defined by the angles of a
right triangle. They also know and are able to use
elementary relationships between them.
Unit 6: SIMILARITY
6.1 – Ratios, proportions, and the geometric mean
6.2 – Use proportions to solve geometry problems
6.3 – Use similar polygons
6.4 – Prove triangles similar by AA
6.5 – Prove triangles similar by SSS and SAS
6.6 – Use proportionality theorems
6.7 – Perform similarity transformations
(Moved to Ch. 9)
Unit 7: RIGHT TRIANGLES & TRIGONOMETRY
Prepare for 8.0
12.0
5.0, 8.0, 11.0
5.0, 12.0
4.0, 5.0
4.0, 7.0
5.0, 11.0
7.1 – Applying the Pythagorean theorem
7.2 – Use the converse of the Pythagorean theorem
7.3 – Use similar right triangles
7.4 – Special right triangles
7.5 – Apply the tangent ratio
7.6 – Apply the sine & cosine ratios
7.7 – Solve right triangles
14.0, 15.0
12.0
4.0, 12.0
20.0
18.0, 19.0, 20.0
18.0, 19.0, 20.0
12.0, 19.0
19.0 – Students use trigonometric functions to solve
for an unknown length of a side of a right triangle,
given an angle and a length of a side.
20.0 – Students know and are able to use angle and
side relationships in problems with special right
triangles, such as 30-60-90 and 45-45-90 triangles.
16.0 – Students perform basic constructions with a
straight edge and compass, such as angle bisectors,
perpendicular bisectors, and the line parallel to a
given line through a point off the line.
FINAL REVIEW
* Preparation for Geometry Standard
CONSTRUCTIONS
1st Semester FINAL EXAM
4 of 6
Updated 7/29/2008
MUHSD Geometry Pacing Guide: 2008-2009 / 3rd Quarter
Dates
Essential Standard Cluster
McDougal Littell Sections
7.0 – Students prove and use theorems involving the
properties of parallel lines cut by a transversal, the
properties of quadrilaterals, and the properties of
circles.
12.0 – Students find and use measures of sides and of
interior and exterior angles of triangles and polygons
to classify figures
7.0 - Students prove and use theorems involving the
properties of parallel lines cut by a transversal, the
properties of quadrilaterals, and the properties of
circles.
17.0 – Students prove theorems by using coordinate
geometry, including the midpoint of a line segment,
the distance formula, and various forms of equations
of lines and circles.
21.0 – Students prove and solve problems regarding
relationships among chords, secants, tangents,
inscribed angles, and inscribed and circumscribed
polygons of circles.
8.0 – Students know, derive and solve problems
involving the perimeter, circumference, area, volume,
lateral area, and surface area of common geometric
figures.
10.0 – Students compute areas of polygons, including
rectangles, scalene triangles, equilateral triangles,
rhombi, parallelograms, and trapezoids.
11.0 – Students determine how changes in dimensions
affect the perimeter, area, and volume of common
geometric figures and solids.
Standard
Resources
Unit 8: QUADRILATERALS
8.1 – Find angle measures in polygons
8.2 – Use properties of parallelograms
8.3 – Show that a quadrilateral is a parallelogram
8.4 – Properties of rhombus, rectangle, square
8.5 – Use properties of trapezoids & kites
8.6 – Identify special quadrilaterals
Unit 10: PROPERTIES OF CIRCLES
12.0
7.0
7.0
7.0
7.0
12.0
10.1 – Use properties of tangents
10.2 – Find arc measures
10.3 – Apply properties of circles
10.4 – Use inscribed angles of polygons
10.5 – Apply other angle relationships in circles
10.6 – Find segment lengths in circles
10.7 – Write and graph equations of circles
7.0, 21.0
7.0
7.0, 21.0
7.0, 21.0
7.0, 21.0
21.0
17.0
Unit 11: MEASURING LENGTH & AREA
11.1 - Areas of triangles and parallelograms
11.2 - Areas of trapezoids, rhombi, and kites
11.3 – Perimeter and area of similar figures
11.4 – Circumference and arc length
11.5 – Areas of circles and sectors
11.6 – Areas of regular polygons
11.7 – Use geometric probability
8.0, 10.0
8.0, 10.0
8.0, 11.0
8.0
8.0
8.0, 10.0
8.0
QUARTER 3 BENCHMARK
* Preparation for Geometry Standard
5 of 6
Updated 7/29/2008
MUHSD Geometry Pacing Guide: 2008-2009 / 4th Quarter
Dates
Essential Standard Cluster
McDougal Littell Sections
Standard
Resources
Unit 12: SURFACE AREA & VOLUME
8.0 - Students know, derive and solve problems
involving the perimeter, circumference, area,
volume, lateral area, and surface area of
common geometric figures.
9.0 – Students compute the volumes and surface
areas of prisms, pyramids, cylinders, cones, and
spheres; and students commit to memory the
formulas for prisms, pyramids, and cylinders.
12.1 – Explore solids
12.2 – Surface area of prisms & cylinders
12.3 – Surface area of pyramids & cones
12.4 – Volume of prisms & cylinders
12.5 – Volume of pyramids & cones
12.6 – Surface Area & Volume of spheres
12.7 – Explore similar solids
9.0
8.0, 9.0
8.0, 9.0
8.0, 9.0
8.0, 9.0
8.0, 9.0
8.0, 11.0
11.0 – Students determine how changes in
dimensions affect the perimeter, area, and
volume of common geometric figures and solids.
22.0 – Students know the effects of rigid motions
on figures in the coordinate plane and space,
including rotations, translations, and reflections.
16.0 – Students perform basic constructions with
a straight edge and compass, such as angle
bisectors, perpendicular bisectors, and the line
parallel to a given line through a point off the
line.
FINAL REVIEW
* Preparation for Geometry Standard
Unit 9: PROPERTIES OF TRANSFORMATIONS
9.1 – Translate figures and use vectors
9.2* – Use properties of matrices
9.3 – Perform reflections
9.4 – Perform rotations
9.5 – Apply compositions of transformations
9.6 – Identify symmetry
9.7 – Identify and perform dilations
4.8 – Perform congruence transformations
6.7 – Perform similarity transformations
CONSTRUCTIONS
22.0
Prepare for 22.0
22.0
22.0
22.0
22.0
22.0
22.0
5.0, 22.0
16.0
2nd Semester FINAL EXAM
6 of 6
Updated 7/29/2008