Question

PROVE: If two sides of a triangle are congruent then the angles opposite to them are congruent.​

Answer 1

Given :   two sides of a triangle are congruent

To Find :  prove that angles opposite to them are congruent.​

Solution:

Assume that ΔABC

AB and AC are congruent sides

To prove that ∠B ≅ ∠ C

Draw AD Median to BC  Hence  BD ≅CD  

in  ΔABD and Δ ACD

AB ≅ AC   given

AD ≅ AD   Reflexive property (common side )

BD ≅CD    By construction as AD is median to BC  

=> ΔABD ≅ Δ ACD  using SSS congruency

Now corresponding parts of congruent triangles are congruent

Hence ∠B  ≅ ∠ C

QED

Hence Proved

If two sides of a triangle are congruent then the angles opposite to them are congruent.​

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Answer 2

Answer:

henced proved : the angles opposites to them are congruent.