Question

For the following figure, given the two congruent angles$\angle 1\cong \angle 2$. Name two segments that must be congruent.

Short answer

The segment that must be congruent is$\overline{KX}\cong \overline{KY}$.

Step-by-step solution

Step 1. Check the figure.

Consider the figure.

Step 2. Apply the concept of an isosceles triangle.

Property of isosceles triangle states that in an isosceles triangle, sides opposite to equal opposite angles are also congruent.

Step 3. Step description.

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

Thus$\mathrm{\Delta }XKY$ is an isosceles triangle.

Since in an isosceles triangle, sides opposite to these congruent angles will also be congruent thus $\overline{KX}\cong \overline{KY}$

Therefore, the congruent sides are $\overline{KX}\cong \overline{KY}$.