# Homework Help: 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!
The text passage contains a geometric proof problem and a response providing guidance on how to solve it. The problem itself does not contain a direct mathematical question or calculation but rather a proof to be completed. The response offers a hint to solve the problem.
no_question
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Homework Help: 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!
user
The text passage contains a geometric proof problem and a response providing guidance on how to solve it. The problem itself does not contain a direct mathematical question or calculation but rather a proof to be completed. The response offers a hint to solve the problem.

TYPE: NO_QUESTION