SOLUTION: If you are given ΔQSU is isosceles with base line ___. QU ___ ___ RQ ≅ TU ∠RQS ≅ ∠TUS ___ PROVE: S IS THE MID

Algebra ->  Geometry-proofs -> SOLUTION: If you are given ΔQSU is isosceles with base line ___. QU ___ ___ RQ ≅ TU ∠RQS ≅ ∠TUS ___ PROVE: S IS THE MID      Log On


   

Question 763284: If you are given ΔQSU is isosceles with base line
___.
QU
___ ___
RQ ≅ TU
∠RQS ≅ ∠TUS
___
PROVE: S IS THE MIDPOINT OF RT
HOW DO I PROVE THIS IN A GEOMETRY PROOF?
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
I'm not able to draw a picture for the problem, but here is the solution.
Consider the 2 triangles RQS and TUS
RQ = TU (given)
SQ = SU (since QSU is an isosceles triangle)
Angle RQS = Angle TUS (given)
Thus we see that 2 sides and the included angle in the 2 triangles are equal. Hence, by the Side-Angle-Side (SAS) theorem, the 2 triangles are congruent.
Therefore, RS = ST (corresponding sides of congruent triangles)
And so, S is the midpoint of RT.
:)