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