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Foundations of Geometry
- Apply postulates about points, lines, and planes.
- Solve problems involving segments, rays, and angles.
- Write formal geometric proofs.
- Apply inductive reasoning, deductive reasoning, and axiomatic systems.
Triangles, Parallel Lines, and Polygons
- Identify different types of triangles.
- Apply the properties of congruent triangles.
- Use properties of parallel lines, transversals, and angles.
- Solve problems involving angles and sides of polygons.
Quadrilaterals, Similar Polygons, and the Pythagorean Theorem
- Apply the triangle inequality theorem.
- Identify the properties of different quadrilaterals.
- Use the properties of special quadrilaterals.
- Use the properties of similar polygons.
- Solve problems involving the Pythagorean Theorem.
Circles and Areas of Polygons
- Use the properties of circles and related components.
- Classify the measure of inscribed angles and arcs.
- Solve problems involving chords, secants, and tangent of circles.
- Calculate the area of polygons.
Introduction to Solid Geometry
- Describe the behavior of lines and planes in space.
- Solve problems involving components of solid figures.
- Calculate the surface area of solids.
- Calculate the volume of solids.
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