Geometry [Honors] (1st semester)

Course Description

Geometry [Honors] gives students a strong foundation in the subject as they formulate mathematical arguments and create geometric constructions. The course begins with a study of points, lines, planes, segments, and angles. Students practice an essential geometric skill: constructing and analyzing a variety of proofs. An in-depth coverage of triangles begins as students explore congruent triangles; special parts including bisectors, medians, and altitudes; and triangle theorems. Students then explore more shapes and calculate area, perimeter, and midsegments. Similarity is covered next, as students work with similarity tests for triangles, ratios, and scale drawings. Students explore geometry on the coordinate plane as they perform transformations and create tessellations. Trigonometric ratios and the laws of sines and cosines are used to solve problems. An in-depth study of circles follows, including sectors, inscribed angles, special arcs, and tangents. Students extend their knowledge to conic sections and three-dimensional figures as they work with surface area, volume, density based modeling, and design problems.

Course Breakdown

• Types of lines
• Classifying triangles
• Patterns and conjectures
• Geometric and algebraic proofs
• Truth tables
• Angles formed by a transversal
• Parallel and perpendicular line construction
• Inscribed shapes inside triangles and circles
• SSS, SAS, and ASA postulates
• Triangle congruency
• Similarity tests

Course Goals

1. Apply geometric properties and relationships through inductive and deductive reasoning.
2. Explain the building blocks of geometry, including using definitions and coordinate geometry.
3. Apply the properties of parallel and perpendicular lines.
4. Perform geometric constructions.
5. Solve problems using the properties of triangles.
6. Prove geometric properties and relationships about parallelograms and quadrilaterals by solving problems and using deductive reasoning.
7. Identify and use the properties of similar polygons and triangles.