Question

which of the following statements is false? 6 is congruent to 7 1 is congruent to 3 2 is congruent to 7 3 is congruent to 6

Explanation:

Step1: Recall angle - congruence rules for parallel lines cut by a transversal

When two parallel lines are cut by a transversal, vertical angles are congruent, corresponding angles are congruent, alternate - interior angles are congruent, and alternate - exterior angles are congruent.

Step2: Analyze each option

• $\angle6$ and $\angle7$ are vertical angles. Vertical angles are always congruent, so $\angle6\cong\angle7$.
• $\angle1$ and $\angle3$ are vertical angles. So, $\angle1\cong\angle3$.
• $\angle2$ and $\angle7$ are neither vertical, corresponding, alternate - interior, nor alternate - exterior angles. They are not congruent in general.
• $\angle3$ and $\angle6$ are alternate - interior angles. For parallel lines cut by a transversal, alternate - interior angles are congruent. So, $\angle3\cong\angle6$.

Answer:

$\text{2 is congruent to 7}$