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Magazine Chapter 3: Q18. (page 107)
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 sides, then the angles opposite those sides are congruent.
Short Answer
If a triangle has two congruent sides, then the angles opposite those sides 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 , in which .
Step 2. Prove ∠B≅∠C.
Consider the definition of isosceles triangles. An Isosceles triangle is a triangle wherein two sides are congruent and also angle opposite to those two congruent sides are also congruent.
So according to above definitions,
If , then must be isosceles triangles.
Step 3. State the conclusion.
As per the definition of Isosceles Triangle, it concludes that, if, then also.
Therefore, if a triangle has two congruent sides, then the angles opposite those sides are congruent is true.
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