Geometric Proof

Question

Write a complete two-column proof for the following information. Hint: Use the Angle Addition Theorem and the fact that a line is made up of two opposite rays.

Given: m∠1 = 62° and lines t and l intersect

Prove: m∠4 = 62°

Answer 1

So, you need to prove the Vertical Angle Theorem.

STATEMENTS REASONS

1.Lines t and l intersect to form vertical angles 1 and 4 1. Given

2.<1 and <3 are form a linear pair, <3 and <4 form 2. Definition of a linear pair

a linear pair

3.<1 and <3 are supplementary, <3 and <4 are 3. Linear Pair Postulate

are supplementary

4.m<1 + m<3 = 180, m<3 + m<4 = 180 4. Definition of Supplementary Angles

5.m<1 + m<3 = m<3 + m<4 5. Transitive Property

6.m<1 = m<4 6. Subtraction Property

7.<1 is congruent to <4 7. Definition of Congruence