Question

For the following figure, complete the statement about the diagram. Then state the definition, postulate or theorem that justify the answer.

If $\angle 2\cong \angle 3$ then$\overline{EC}\cong \_\_$.

Short answer

The statement is$\overline{EC}\cong \overline{EB}$.

Step-by-step solution

Step 1- Check the figure.

Consider the figure.

Step 2- Apply the concept of the isosceles triangle theorem.

The isosceles triangle theorem states that if two sides of a triangle are congruent, then angles opposite those sides are congruent and if angles opposite those sides are congruent, then two sides of a triangle are equal..

Step 3- Step description.

Sincethe sides opposite to equal angles are equal and here, angles 2 and 3 are equal thus EC is equal to EB.

Thus, the statement is$\overline{EC}\cong \overline{EB}$ and the theorem is isosceles triangle theorem.