Question

select the correct answer.
in the given diagram, ( m parallel n ).
prove: ( angle 1 cong angle 5 )
which statement is missing in the proof?
a. ( m angle 5 + m angle 7 = 180 ^ { circ } )
b. ( angle 1 cong angle 6 )
c. ( angle 7 cong angle 5 )
d. ( angle 3 cong angle 7 )

Explanation:

Step1: Recall vertical angles theorem

Vertical angles are congruent. In the diagram, \(\angle7\) and \(\angle5\) are vertical angles.

Step2: Check transitive property

We know \(\angle1\cong\angle7\) (from alternate exterior angle theorem) and if \(\angle7\cong\angle5\) (vertical angles theorem), then by transitive property \(\angle1\cong\angle5\)

Answer:

C. \(\angle7\cong\angle5\)