Question

The isosceles triangle theorem says "If two sides of a triangle are congruent then the angles opposite those sides are congruent If you are using this figure to prove the isosceles triangle theorem, which of the following would be the best strategy

Answer 1

Answer: Draw QS so that S is the midpoint of PR, then prove PQS=RQS using SSS

Explanation:

Answer 2

(A) option A is correct that is draw TV so that V is the mid point of SU, then prove ΔSTV≅ΔUTV using SSS.

Explanation:

From the given figure, it is given that ST=TU, then draw TV so that V is the mid point of SU, then, from

ΔSTV and ΔUTV

ST=UT (Given)

SV=UV (Definition of mid point)

TV=TV (Reflexive property)

Thus, by SSS rule

ΔSTV≅ΔUTV

Hence, by CPCTC, ∠S≅∠U which satisfies the isosceles triangle theorem that is "If two sides of a triangle are congruent then the angles opposite those sides are congruent".

Thus, option A is correct that is draw TV so that V is the mid point of SU, then prove ΔSTV≅ΔUTV using SSS.