Question 762096: If you have triangle QSU is isosceles with base QU. RQ is congruent with TU and angle RQS is congruent with angle TUS. How do I prove S is the midpoint of RT?The first two steps would be the given correct? Then the next three would have to be congruent statements correct? So would I use the base angle theorem, base angle converse theorem and SAS as the three congruency statements?
Answer by ramkikk66(644)   (Show Source):
You can put this solution on YOUR website! Compare the 2 triangles RQS and TUS
1) It is already given that RQ = UT
2) SQ = US, because QSU is an isosceles triangle
3) Included angle RQU = TUS (given)
SAS or Side-angle-side theorem states that if 2 sides and the included angle of 2 triangles are equal, the triangles are congruent.
By SAS theorem, the triangles RQS and TUS are congruent.
So, RS = ST (corresponding sides of congruent triangles are equal)
Therefore, S is the midpoint of RT.
Hope this helps.
:)
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