Chapter 4.4, Problem 5CE

To determine

To find:The two segments that are congruent to each other, given two congruent angles.

Answer to Problem 5CE

  $\overline{KX}\cong \overline{KY}$

Explanation of Solution

Giveninformation:In the given figure, $\angle 1\cong \angle 2$ .

  

Conceptused:In an isosceles triangle, sides opposite to equal opposite angles are also congruent.

Calculation:

In $\Delta XKY$ , $\angle 1\cong \angle 2$ , that is, the base angles are congruent.

Thus, $\Delta XKY$ is an isosceles triangle. Now, the sides opposite to these congruent angles will also be congruent. So, in this triangle,

  $\overline{KX}\cong \overline{KY}$

Conclusion: The sides $\overline{KX}$ and $\overline{KY}$ are congruent to each other.