The proof of the Converse of the Alternate Interior Angles Theorem below looks different than any proof you have seen so far in this course. You know two forms of proof—paragraph and two-column. In a third form, called flow proof, arrows show the logical connections between the statements. Reasons are written below the statements.
Proof
Proof of Theorem 3-4: Converse of the Alternate Interior Angles Theorem
Given:
Prove:
Proof: Problem 2 Writing a Flow Proof of Theorem 3-6
Given:
Prove:
| Know | Need | Plan |
|---|---|---|
|
One pair of corresponding angles congruent to prove
|
Use a pair of congruent vertical angles to relate either
|
✓ Got It?
- Use the same diagram and given information from Problem 2. Prove that
Table of Contents
- 6-1 The Polygon Angle-Sum Theorems
- 6-2 Properties of Parallelograms
- 6-3 Proving That a Quadrilateral Is a Parallelogram
- 6-4 Properties of Rhombuses, Rectangles, and Squares
- 6-5 Conditions for Rhombuses, Rectangles, and Squares
- 6-6 Trapezoids and Kites
- 6-7 Polygons in the Coordinate Plane
- 6-8 and 6-9 Coordinate Geometry and Coordinate Proofs