MAT 122, Geometry

1. Use definitions, postulates, and previously proven theorems to prove basic geometric relationships deductively, using a two-column “statements and reasons” format.
2. Prove the congruence of two triangles by using sss, sas, asa, or aas as appropriate.
3. Prove the congruence of two line segments or angles by locating them in various triangles and then establishing the congruence of those triangles.
4. Use the method of indirect proof to establish the truth of a proposition by demonstrating that the assumption of the truth of its negation results in a contradiction.
5. Prove various geometric propositions that involve quadrilaterals, parallel lines, circles, and parts of circles by using their definitions and properties.
6. Prove the similarity of two triangles by using aa
7. Recognize and use appropriately the various proportions that are valid when two polygons are known to be similar.
8. State the Pythagorean theorem and use it to solve right triangles.
9. State and use the relationship that exists between the lengths of the sides of any 30-60 right triangle.
10. State and use the relationship that exists between the lengths of the sides of any 45-45 right triangle.
11. Define the three primary trigonometric functions of an acute angle of a right triangle and use these trigonometric functions to solve word problems.
12. Find the areas of the common shapes of plane geometry, including being able to find the area of a triangle by using Heron’s formula.
13. Find the slope of a line and use it to write an equation of the line.
14. Graph linear equations.
15. Find the distance between two points in a rectangular coordinate system and find the coordinates of the point that is midway between the two points.
16. Use a compass and a straightedge to perform the fundamental geometric constructions.