Question

prove that alternate interior angles 3 and 6 are congruent. vertical angles are congruent. transitive property of congruence. supplementary angles sum to 180m∠5 = 180° - m∠6 ∠2 ≅ ∠3 corresponding angles are congruent∠8. ≅ ∠6 statement reason ∠2 ≅ ∠6

Explanation:

Step1: Identify corresponding - angle property

Assume we have parallel lines cut by a transversal. If the lines are parallel, corresponding angles are congruent. Let's assume $\angle2\cong\angle6$ because they are corresponding angles.

Step2: Identify vertical - angle property

We know that vertical angles are congruent. Given $\angle2\cong\angle3$ since they are vertical angles.

Step3: Use transitive property

By the transitive property of congruence, if $\angle2\cong\angle6$ and $\angle2\cong\angle3$, then $\angle3\cong\angle6$.

Statement	Reason
$\angle2\cong\angle3$	Vertical angles are congruent
$\angle3\cong\angle6$	Transitive property of congruence

Answer:

The proof is shown in the above - constructed two - column proof with statements and corresponding reasons. The key steps are using the properties of corresponding angles, vertical angles, and the transitive property of congruence to show that alternate interior angles $\angle3$ and $\angle6$ are congruent.