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!