Question

which of the following correctly justifies statement 4 of the two - column proof? given (overline{jk}paralleloverline{lm}) prove (angle2congangle7) statement justification 1 (overline{jk}paralleloverline{lm}) 1 given 2 (angle6congangle7) 2 3 (angle2congangle6) 3 4 (angle2congangle7) 4 corresponding angles theorem transitive property of equality vertical angles theorem substitution property of equality

Explanation:

Step1: Recall the given equal - angle statements

We have $\angle6\cong\angle7$ (Statement 2) and $\angle2\cong\angle6$ (Statement 3).

Step2: Apply the transitive property of equality

If $a = b$ and $b = c$, then $a = c$. Here, $a=\angle2$, $b = \angle6$ and $c=\angle7$. So, if $\angle2\cong\angle6$ and $\angle6\cong\angle7$, then $\angle2\cong\angle7$.

Answer:

Transitive Property of Equality