| 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 to complement geometric principles.
PREREQUISITE:
One credit in Algebra I and departmental approval
TEXT:
Geometry. 1998, Burrill, Cummins, Kanold, Boyd, and Malloy
BENCHMARKS:
The students will be able to:
1. Name and recognize symbolic expressions for geometric figures.
2. Write and determine truth of conjunctions and disjunctions.
3. Use theorems, postulates, properties, and definitions to write proofs.
4. Use knowledge of geometric principles to make constructions.
5. Solve geometric problems using algebra.
6. Classify triangles based on side length and angle measures.
7. Identify, name, and categorize polygons.
8. Find angle measures and number of sides of a polygon.
9. Identify necessary and sufficient conditions for special quadrilaterals.
10. Solve proportions.
11. Identify similar polygons.
12. Determine midpoint, slope, and equations of a line.
13. Graph equations of a line.
14. Solve for lengths and angle measures of a right triangle.
15. Solve word problems using trigonometric ratios.
16. Identify arcs, special segments, lines, and other points related to circles and spheres.
17. Find area of polygons and circles.
18. Find area and volume of basic three-dimensional figures.
Unit Topic
1 Tools of Geometry
Segments and Angles
Congruence
Constructions
Conjunctions and Disjuctions
2 Foundations of Geometry
Conditional Statements
Theorems and Postulates
Inductive and deductive Reasoning
Drawing Conclusions
Introduction to Proofs
3 Angles and Lines
Angles of a Triangle
Vertical Angles and Angle Bisectors
Parallel Lines, Transversals, and Angles
Parallel Line Postulates and Theorems
4 Congruent Triangles
Triangle Classification
Congruent Triangles
Corresponding Parts
Overlapping Triangles
Inequalities for Two Triangles
5
Polygons
Properties of Polygons
Interior and Exterior Angles
Quadrilaterals and Parallelograms
6 Special Quadrilaterals
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
Rectangles and Squares
Parallelograms
Triangles
Trapezoids
Regular Polygons
Circles
Arc Length and sector Area
12
Area, Surface Area, and Volume
Prisms and Cylinders
Pyramid and Cones
Spheres
1. Textbook
2. Teacher-Prepared Materials
3. Computers
1. Tests
2. Quizzes
3. Projects
4. Notebooks