Question

given: \\( \angle 6 \cong \angle 3 \\) prove: \\( \ell \parallel m \\) statements reasons 1. \\( \angle 6 \cong \angle 3 \\) 1. 2. 2. vertical angles theorem 3. \\( \angle 6 \cong \angle 2 \\) 3. 4. \\( \ell \parallel m \\) 4. converse of the corresponding angles postulate a. transitive property of congruence b. \\( \angle 3 \cong \angle 2 \\) c. given d. \\( m \angle 3 = m \angle 2 \\) e. congruent supplements theorem

Explanation:

Step1: Fill in Reason 1

Given in the problem statement.

Step2: Fill in Statement 2

By Vertical Angles Theorem, \(\angle3\cong\angle2\).

Step3: Fill in Reason 3

Since \(\angle6\cong\angle3\) (Given) and \(\angle3\cong\angle2\) (Vertical Angles Theorem), by Transitive Property of Congruence \(\angle6\cong\angle2\).

Answer:

1. c. Given
2. b. \(\angle3\cong\angle2\)
3. a. Transitive Property of Congruence