Question

Draw several diagrams to help you decide whether each statement is true or false. If it is false, show a counterexample. It is true, draw and label a diagram you could use in a proof. List, in terms of the diagram, what is given and what is to be proved. Do not write a proof.

If a triangle has two congruent angles, then the sides opposite those angles are congruent.

Short answer

If a triangle has two congruent angles, then the sides opposite those angles are congruent istrue.

Step-by-step solution

Step 1. Draw the diagram.

Draw a diagram of a triangle with two congruent sides.

In above figure there is $\Delta ABC$, in which $\angle B\cong \angle C$.

Step 2. Prove AB≅AC.

two sides are congruent and also angle opposite to those two congruent sides is also congruent.

So according to the above definitions,

If $\angle B\cong \angle C$, then$\Delta ABC$ must be isosceles triangles.

Step 3. State the conclusion.

As per the definition of the Isosceles Triangle, it concludes that, if $\angle B\cong \angle C$, then also $AB\cong AC$.

Therefore, if a triangle has two congruent angles, then the sides opposite those angles are congruent is true.