indirect proof geometry

[jen1990]

I have to write an indirect proof. This is what I have so far:
Assume temporarily that triangle RST is not isosceles. Then RU=RU and angle RUS=angle RUT and angle SRU=angle TRU.

Then I'm lost. :?


thanks.

 

[soroban]

Hello, jen1990!

You're almost there . . .

You <u>assumed</u> that triangle RST is not isosceles.

Then we are given: \(\displaystyle RU=RU\) and \(\displaystyle \angle RUS\,=\,\angle RUT\) and \(\displaystyle \angle SRU\,=\,\angle TRU\)

Then: \(\displaystyle \Delta RUS\) is congruent to \(\displaystyle \Delta RUT\) by a.s.a.

Hence: \(\displaystyle RS\,=\,RT\) (corresponding parts of congruent triangles)
. . . . . . and \(\displaystyle \Delta RST\) is isosceles.

We have reached a contradiction.
Therefore, your original assumption must be incorrect.

 

[jen1990]

thank you so much!