1. Foundations of Geometry
- I will be able to see the important role that logic plays in our lives.
- I will learn to develop airtight arguments, and prove that I’m right.
- I will be able to identify when triangles are similar (scaled up or down) and when triangles are congruent (exactly the same shape and size).
- I will be able to use the properties of triangle angles and altitudes to calculate the distance to far-away objects.
3. Right Triangles
- I will be able to identify right triangles and special right triangles (30-60-90 and 45-45-90).
- I will be able to apply the Pythagorean theorem to find missing sides and angles of right triangles.
- I will be able to identify and use postulates SSS, SAS, ASA to prove congruence.
- I will learn what SOH CAH TOA means and how to use it to find missing angle measures and side lengths.
- I will be able to use two methods to solve for missing parts of oblique triangles (the law of cosines and the law of sines).
- I will be able to solve problems involving all kinds of triangles, not just right ones.
5. Quadrilaterals and Other Polygons
- I will be able to identify shapes in the real world.
- I will learn the names of polygons, and how to find their perimeters, areas, and angles.
- I will be able to draw diagonals and interior triangles, and identify patterns.
- I will be able to identify quadrilaterals (four-sided polygons), as well as parallelograms, rhombi, squares, and rectangles.
6. Circles Without Coordinates
- I will learn how to calculate the area of a circle.
- I will be able to identify the properties, and measure, the parts of a circle, such as radii, diameters, arcs, and intercepted angles.
- I will be able to use inscribed angles and polygons to calculate angles within a circle formed by chords, secants, and tangents.