Given: AQRS = ATRS R Q T S Prove: AQST is isosceles

Question

asked Nov 23, 2023 112k views

1 Answer

Dustin Silk · Answer 1 · 2023-11-28T23:47:44+0000

we know that

If two triangles are congruent, then its corresponding angles and its corresponding sides are congruent

In this problem

triangle QRS and TRS are congruent -------> given

so

that means

by definition of congruence

QR=TR ---> by definition of congruence

RS=RS ---> by definition of congruence

QS=TS ---> by definition of congruence

Remember that

A triangle isosceles has two equal sides and two equal interior angles

In the triangle QST we have

QS=TS

and that means-----> the triangle has two equal sides and two equal interior angles

therefore

QST is an isosceles triangle