mth535 | Graduate
topic title goes here
Foundations of Geometry, Triangles
- Classify triangles by their sides and by their angles.
- Prove how triangles are congruent using geometric theorems.
- Construct a triangle congruent to a given triangle.
- Use congruent and right triangles to prove statements and theorems.
- Define deductive or inductive reasoning and proofs, and axiomatic systems.
- Identify points, lines, and planes.
- Describe segments, rays, and angles.
- Formulate geometric proofs.
Parallel Lines and Polygons, Quadrilaterals
- Define parallel lines, transversals, and angles.
- Describe the characteristics of a quadrilateral.
- Apply the properties of parallelograms.
- Use the properties of special quadrilaterals (e.g., parallelogram, rectangles, squares, rhombus, and kite).
- Examine the properties of trapezoids.
- Identify different types of polygons and their components.
- Review topics and objectives from all weeks.
Similar Polygons and the Pythagorean Theorem
- Define ratio, proportion, and proportional segments.
- Apply the postulates and theorems of similar polygons.
- Construct proportional segments of polygons.
- Demonstrate the applications of the Pythagorean Theorem.
- Define a circle and related terms (e.g., arcs, semi-circles, inscribed angles).
- Describe the theorems of chords and secants of circles.
- Construct a tangent to a circle and measure angles formed by tangents.
Areas of Polygons and Circles
- Determine areas of quadrilaterals.
- Calculate circumference and area of circles.
- Identify area and arc length of a sector.
- Apply the area formula to regular polygons.
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