# Geometric proof.

1. Aug 24, 2010

### Sirsh

Hello all, the picture i have attached is the question.
http://img842.imageshack.us/img842/8921/geometricproof.png [Broken]

I've concluded that there are two i isosceles triangles in this one triangle.

$$\angle$$PSQ + $$\angle$$QSR = 90degrees
Finding the angle in one of the isosceles triangles.

$$\Delta$$RQS with RQ = SQ
RQ = SQ (given)
If we put a line through the isosceles triangle and call this Z.
RZ = SZ
RZ = SZ (common to both)
therefore: $$\Delta$$RZQ =~ $$\Delta$$SZQ
therefore: $$\Delta$$QRZ = $$\Delta$$QSZ
which results in: $$\angle$$QRS = $$\angle$$QSR

Last edited by a moderator: May 4, 2017
2. Aug 24, 2010

### Rajini

Hi,
I dont understand your explanation on 'Z'!
But your starting point is correct..You have two isosceles triangles (PSQ and QSR) in the triangle PSR.
I will now give you a easy hint:
First consider the isosceles triangle PSQ and find which two angles are equal?
Then take the second isosceles triangle QSR and find which two angles are equal?
Now you know the three angles of the triangle PSR = 180 degree.
Got it!