Question

The isosceles triangle theorem states that if two sides of a triangle are congruent, then the angles _____________ those sides are congruent.

Answer 1

the answer is opposite

Answer 2

Answer: The isosceles triangle theorem states that if two sides of a triangle are congruent, then the angles opposite to those sides are congruent.

Explanation:

Isosceles triangle theorem : If two sides of a triangle are congruent , then the angles opposite to these sides are congruent.

Consider an isosceles triangle ABC

Let D is the midpoint of triangle BC

Then, BD=CD

AD=AD[Reflexive Property ],

AB=AC [Definition of isosceles triangle]

Therefore, by SSS postulate ,

ΔADB≅ΔADC

Since corresponding parts of congruent triangles are congruent,

∴ ∠B≅∠C Hence Proved

Therefore, The isosceles triangle theorem states that if two sides of a triangle are congruent, then the angles opposite to those sides are congruent.