Benchmarks Content Resources Assessment
COURSE DESCRIPTION: This course acquaints the student with the basic geometric figures and their properties and leads to abstract reasoning using proofs. Algebra is used throughout to complement geometric principles. The final quarter is devoted to the study of trigonometry.
PREREQUISITE: One credit in Honors Algebra II with a grade of “B” or better and departmental approval
TEXTS: Geometry. 1998, Burrill, Cummins, Kanold, Boyd, & Malloy
Trigonometry. 1975, Dressler, Isidore & Rich, Barnett
BENCHMARKS:
The students will be able to:
1. Name and recognize symbolic expressions for geometric figures.
2. Use theorems, postulates, properties, and definitions to write proofs.
3. Use knowledge of geometric principles to make constructions.
4. Solve geometric problems using algebra.
5. Classify triangles based on side length and angle measures.
6. Identify, name, and categorize polygons.
7. Identify necessary and sufficient conditions for special quadrilaterals.
8. Solve proportions.
9. Identify similar polygons.
10. Determine midpoint, slope, and equations of a line.
11. Graph equations of a line.
12. Solve for lengths and angle measures of a right triangle.
13. Solve problems using trigonometric ratios.
14. Find area of polygons and circles.
15. Find area and volume of three-dimensional figures.
16. Solve triangles using the laws of sines and cosines.
17. Convert degree measure to radian measure.
18. Find arc lengths and sector areas for circles.
19. Find angular velocity for rotating systems.
20. Prove trigonometric identities.
Unit Topic
1 Tools of Geometry
Segments and angles
Congruence
Constructions
2 Foundations of Geometry
Conditional statements
Theorems and postulates
Inductive and deductive reasoning
Introduction to proofs
3 Angles and Lines
Angles of a triangle
Vertical angles and angle bisectors
Parallel line postulates and theorems
4 Congruent Triangles
Triangle classification
Congruent triangles
Corresponding parts
Inequalities for two triangles
5 Polygons
Properties of polygons
Interior and exterior angles
Quadrilaterals and parallelograms
6
Special Quadrilaterals
Parallelograms
Rectangles, rhombuses, and squares
Trapezoids
7 Similarity
Ratios and proportions
Similar polygons
8 Right Triangles
Pythagorean theorem
Special right triangles
Trigonometric ratios
9 Coordinate Geometry
Distance formula
Slope of a line
Midpoint formula
Equations of a line
10 Circles
Arcs and central angles
Chords
Inscribed angles
Angles formed by secants and tangents
Equations of circles
11 Area
Parallelograms
Triangles
Trapezoids
Regular polygons
Circles
Arc length and sector area
12 Area, Surface Area, and Volume
Prisms and cylinders
Pyramid and cones
Spheres
13 Radian Measure and Circular Functions
Applications of radian measure
Circular functions of real numbers
Linear and angular velocity
Graphs of circular functions
14 Trigonometric Identities
Verifying trigonometric identities
Sum and difference identities
Double and half-angle identities
15 Applications of Trigonometry
Law of Sines
Law of Cosines
Trigonometric equations
1. Textbook
2. Teacher-prepared materials
3. Computer
1. Tests
2. Quizzes
3. Class work
4. Homework