Chapter 4, Problem 11CR

To determine

To Find: the segments which must be congruent in the given figure below such that $\angle 3\cong \angle 4$ .

Answer to Problem 11CR

  $\overline{RE}\cong \overline{VE}$

Explanation of Solution

Given

Given figure,

  

And $\angle 3\cong \angle 4$ .

Concept used:

If two angles of a triangle are congruent, then the sides opposite to those angle are congruent

Calculation:

Using theorem which states-

If two angles of a triangle are congruent, then the sides opposite to those angle are congruent.

Consider triangle $\Delta ERV$ ,

Since, $\angle 3\cong \angle 4$ , $\overline{RE}$ and $\overline{VE}$ are sides opposite to angle $\angle 4$ and $\angle 3$ respectively.

Therefore, $\overline{RE}\cong \overline{VE}$ .

Therefore, answer is $\overline{RE}\cong \overline{VE}$