## anonymous 4 years ago Geometry Question: How do I prove a triangle isosceles when there is a rectangle placed in the middle of it?

1. anonymous

Give the drawing

2. anonymous

i forgot one thing

3. anonymous

it is not necessarily isoceles till you make clear what middle imples.

4. anonymous

|dw:1328375071307:dw|

5. anonymous

properties of a rectangle apply

6. jhonyy9

what sign exactly ,,in the middle of it " ? ... middle of two lateral sides ?

7. anonymous

This is the picture I am given, and i have to prove the triangle isosceles

8. anonymous

Use congruence of triangles to proves that tir(GPH) and tri(KMJ) are congruent by RHS condition. Now use fact that corresponding angles of congruent tringles are equal to show Base angles of triangle are equal . Hence proved

9. anonymous

I know that I have to prove the triangles congruent and then I can just use cpctc to prove the triangle isosceles, but I do not know what rhs condition is. -__-

10. anonymous

Both triangles must be right angles-R have one side equal -S hve hypotenetuse Equal-H

11. anonymous

Oh right! hypotenuse leg! I forgot! thanks a lot

12. anonymous

|dw:1328375404823:dw| mk=GP , mj=ph and h=j 90 degree now pgm = mjk if pgm = mjk then k=G if k=G then ogk is isosceles

13. anonymous

|dw:1328386560821:dw|

14. jhonyy9

so because HP equal MJ from this result that angle G equal angle K so from this result that the triangle GOK is isosceles

15. jhonyy9

- so this is the shorter prooff and easy