Question

ΔABC and ΔXYZ are both isosceles such that AB≅AC and XY≅XZ. If AB ≅ XY and BC≅YZ, Prove that ΔABC and ΔXYZ are congruent. State the condition of congruency.

Answer 1

Step-by-step explanation:

Given: ΔABC and ΔXYZ are both isosceles

           AB=AC

           XY=XZ

           AB=XY

           BC=YZ

To Prove: ΔABC≅ΔXYZ

Proof: In ΔABC and ΔXYZ,

           AB=XY (Given)

           AB=AC and XY=XZ

Now,   AC=XZ  (as AB=XY)

           BC=YZ (Given)

Therefore, ΔABC≅ΔXYZ (By SSS congruency criterion)