Geometry

Course Description

Open to: Grades 10, 11, 12 One Year Course
Prerequisite: C or better in Algebra 1, or pass Intermediate Algebra 1, Instructor/Counselor approval
Content: Students will use an integrated approach to concepts of algebra, geometry, logic and probability with emphasis on geometry.

Adopted Materials

Title: Geometry
Edition: 2004
Publisher Glencoe
ISBN: 0-07-829637-4

Mathematics Curriculum Map
Course overview, activities, vocabulary, supplemental materials in pdf format.

Copyright Resources

Course Scope

• Download this curriculum as a "Printer Friendly" pdf file

Unit 1

Points, Lines, Planes & Angles

2 weeks

0821.01 Use calculation and measurement with relationship to points, lines, and shapes within a plane.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Describe the relationships between points, lines and planes.

p. 8, 22

TMA

02

Classify angles according to their degree measure.

p. 30

TMA, EOC

03

Find numerical unknowns related to the coordinate plane (e.g., distance, midpoint).

pp. 21, 22,

TMA, EOC

04

Measure segments and angles with precision

p. 13, 29

TO, TMA

05

Construct, using a straightedge and compass, a two-dimensional figure from a set of instructions.

p. 15, 31, 33

TO, TMA, EOC

06

Identify special angle relationships (linear pair, vertical, complementary, supplementary).

p. 37, 39

TMA, EOC

Back to Top

Unit 2

Reasoning & Proof

2½ weeks

0821.02 Understand and use a variety of reasoning and problem solving skills.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Apply inductive and deductive reasoning.

p. 62, 82

EOC, TMA

02

Define and apply terms associated with mathematical logic and reasoning (e.g. hypotheses, conclusion, conditional, counterexample).

p. 62, 67,68, 75, 81, 83, 89.

EOC, TMA

03

Use properties from algebra and geometry to begin developing formal proofs.

p. 94

TO, TMA

Back to Top

Unit 3

Parallel & Perpendicular Lines

3 weeks

0821.03 Understand and apply the relationships between parallel and perpendicular lines.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Compare the slopes of parallel and perpendicular lines.

p. 139-141

EOC, TMA

02

Find equations of lines.

p. 145-147

EOC, TMA

03

Define and apply terms associated with mathematical logic and reasoning.

p. 151-153

EOC, TMA

04

Read and write a two-column proof and identify statements that do not logically follow from the preceding statements.

p. 151-153

EOC, TMA

05

Solve for missing angles in problems involving parallel lines cut by a transversal.

p. 126-128

ECO, TMA

06

Prove that two lines are parallel.

p. 151-153

EOC, TMA

Back to Top

Unit 4

Congruent Triangles

3½ weeks

0821.04 Describe, classify and prove relationships between triangles.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Identify and classify triangles by their angle measure and side lengths. (e.g., acute, obtuse, right, scalene, isosceles, equilateral.)

p. 178-179, 216-218

EOC, TMA

02

Find angles related to triangles-interior/exterior.

p. 186

EOC, TMA

03

Describe and apply the congruence relationships. for triangles (e.g., SSS, SAS, ASA, AAS, HL.)

p. 192-194, 200-202, 207-209

EOC, TMA

04

Use CPCTC in congruence relationships.

pp. 192-194

EOC, TMA

Back to Top

Unit 5

Relationships in Triangles

2 weeks

0821.05 Described and classify special segments in triangles; apply inequalities to angles and sides of triangles.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Identify parts of triangles. (e.g. hypotenuse, angle bisector, altitude, perpendicular bisector, median, incenter, orthocenter, circumcenter, centroid.)

p. 236-246

EOC, TMA

02

Use the triangle inequality theorem to solve problems involving triangles.

p. 261-263, 267-270

EOC, TMA

03

Recognize and apply properties of inequalities to the relationships between angles and sides of a triangle.

p.247-250

EOC, TMA

Back to Top

Unit 6

Proportions & Similarity

2 weeks

821.06 Apply proportions in similar figures to solve problems.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use ratios and proportions to solve problems.

p. 282-284

EOC, TMA

02

Prove triangles are similar. (e.g., AA~, SSS~, SAS~)

p. 298-300

EOC, TMA

03

Apply ratios and proportions to solve problems involving similar figures.

p. 307-310, 316-317

EOC, TMA

04

Know and apply the properties of a midsegment.

p. 306

EOC, TMA

Back to Top

Unit 7

Right Triangles & Trig

4½ weeks

0821.07 Apply the geometry of right triangles.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Understand the basic concepts of right triangle trigonometry; basic trigonometry ratios of sine, cosine and tangent.

p. 371-373,

EOC, TMA

02

Solve for parts of right triangles using the geometric mean.

p. 342-344

EOC, TMA

03

Use the Pythagorean Theorem and its converse to find missing side lengths and determine whether a triangle is acute, right, or obtuse.

p. 350-353

EOC, TMA

04

Find missing side lengths and angles of special right triangles.

p. 357-360

EOC, TMA

05

Use trigonometric ratios to solve for side lengths and angles.

p. 364-367

EOC, TMA

06

Use the laws of sine and cosine to solve triangles

p. 377-380, 385-388

EOC, TMA

Back to Top

Unit 8

Quadrilaterals

2 - 3 weeks

0821.08 Apply properties of quadrilaterals to solve problems.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Identify, name and classify polygons.

p.

EOC, TMA

02

Find the angles of a polygon and the sum of interior and exterior angles of a polygon.

p. 404-406

EOC, TMA

03

Use properties of parallelograms to solve problems in geometry.

p. 411-414

EOC, TMA

04

Identify and use properties of special parallelograms.

p. 424-427, 431-433,

EOC, TMA

05

Identify and use properties of trapezoids.

p. 439-441

EOC, TMA

06

Prove that quadrilaterals are parallelograms.

p. 417-420

Back to Top

Unit 9

Transformations

2 weeks

0821.09 Use coordinate geometry to solve problems involving transformations.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Identify the result of a specific transformation or kind of transformation used to create a given result.

p.463-466, 470-472, 476-478

EOC, TMA

02

Relate line symmetry to reflections.

p. 466

EOC, TMA

03

Relate rotational symmetry and rotations.

p. 478

EOC, TMA

04

Find magnitudes and directions of vectors.

p. 498-502

EOC, TMA

Back to Top

Unit 10

Circles

3 weeks

0821.10 Identify the parts of a circle and calculate measurements of them.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use vocabulary associated with circles.

p. 522-524

EOC, TMA

02

Find angles and arcs related to circles and segment lengths formed inside and outside circles. (e.g., central and inscribed angles, and angles formed by chords, secants, tangents)

p. 529531, 536-539, 544-548, 552-555, 561-563, 569-571

EOC, TMA

03

Develop the equation of a circle from given information and identify the center and radius of a circle equation.

p. 575-577

EOC, TMA

04

Find the circumference of circles and arc lengths.

p. 523, 530

EOC, TMA

Back to Top

Unit 11

Areas of Polygons & Circles

2 weeks

0821.11 Use formulas to determine planar measurements of polygons and circles.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Find areas and perimeters of polygons.

p. 595-597, 601-604, 610-612

EOC, TMA

02

Calculate the area of circles, sectors and segments of circles.

p. 610-612, 623-624

EOC, TMA

03

Determine how changes in dimensions affect the perimeter and area of geometric figures.

p. 617-618

EOC, TMA

Back to Top

Unit 12

Surface Area

2 weeks

0821.12 Perform calculations for lateral area and surface area of three-dimensional figures.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Identify three-dimensional figures and their parts. (e.g., face, edge, vertex)

p. 636-639

EOC, TMA

02

Calculate the surface area of three-dimensional objects.

p.644, 649-651, 655-656, 640-662, 666-667, 671-673

EOC, TMA

Back to Top

Unit 13

Volume

2 weeks

0821.12 Perform calculations for volume of three-dimensional figures.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Calculate the volume of three-dimensional objects.

p. 688-690, 696-698, 702-703

EOC, TMA

02

Determine how changes in dimensions affect the surface area and volume of three-dimensional figures.

p. 711

EOC, TMA