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Chapter 3: Q19. (page 108)

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

Expert verified

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

Step by step solution

01

Step 1. Draw the diagram.

Draw a diagram of a triangle with two congruent sides.

In above figure there is 螖ABC, in which 鈭�B鈮�鈭�C.

02

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 鈭�B鈮�鈭�C, then螖ABC must be isosceles triangles.

03

Step 3. State the conclusion.

As per the definition of the Isosceles Triangle, it concludes that, if 鈭�B鈮�鈭�C, then also AB鈮�AC.

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

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