Question

given: lines p and q are parallel and r is a transversal
prove: (angle 2congangle 7)
which statements could complete the proof?
a
b
angle 2 is congruent to angle 3
angle 2 is congruent to angle 6
angle 3 is congruent to angle 7
angle 3 is congruent to angle 6

Explanation:

Step1: Analyze Statement A

Since the reason for statement 2 is “vert. $\angle$'s $\cong$” (vertical angles are congruent), vertical angles are formed when two lines intersect. $\angle2$ and $\angle3$ are vertical angles. So, statement A should be $\angle2\cong\angle3$.

Step2: Analyze Statement B

The reason for statement 3 is “corr. $\angle$'s thm.” (corresponding angles theorem). When two parallel lines ($p\parallel q$) are cut by a transversal ($r$), $\angle3$ and $\angle7$ are corresponding angles. So, statement B should be $\angle3\cong\angle7$. Then, by the transitive property (if $a = b$ and $b = c$, then $a = c$), since $\angle2\cong\angle3$ and $\angle3\cong\angle7$, we can conclude $\angle2\cong\angle7$.

Answer:

A. $\angle2\cong\angle3$; B. $\angle3\cong\angle7$