# Prove the angles equal to prove the sides triangle problem

1. Dec 8, 2009

### 1/2"

This is an mensurational problem of triangles.
1. The problem statement, all variables and given/known data
In triangle ABC, anngle B=90degrees and D is the mid point of AC .If AB=20 cm and Bd=14.5cm,find the area and perimeter of the triangle ABC.
My book says that BD=AD=DC=> AC=2BD=29 and so on
But i can't get how could they just write that BD=AD??
I am really at my wits end.
If we take this into consideration it is really easy but how do I do it when I iam not clear at the base.
I tried to prove the angles equal to prove the sides but it's not working.

Last edited: Dec 8, 2009
2. Dec 8, 2009

### Staff: Mentor

Re: Triangle

If the area and perimeter of the triangle ABC do what? We can't help you if you don't give us all of the information in the problem.

3. Dec 8, 2009

### 1/2"

Re: Triangle

I am really sorrrrrry!!

4. Dec 8, 2009

### Staff: Mentor

Re: Triangle

Make a rectangle ABCE by drawing a line segment AE that is parallel to BC and by another line segment CE that is parallel to AB. In my drawing the right angle is on the left, angle A is on the right, and angle C is above the right angle.

Extend the line segment BD to make BE. The segments AC and BE are the diagonals of a rectangle, and they both cross at D. What can you say about the lengths of BD and DE? You already know that AD and DC are equal.

Is that enough to get you going?

5. Dec 12, 2009

### 1/2"

Re: Triangle

So you mean BD=BE
But what next....
(i am really sorry but i am real slow learner)

6. Dec 13, 2009

### 1/2"

Re: Triangle

Is there something wrong i have done??

7. Dec 14, 2009

### Staff: Mentor

Re: Triangle

No, BD != BE. You should have a rectangle ABCE. BE is the length of a diagonal of the rectangle, and AC is the other diagonal. What do you know about the diagonals of a rectangle?

8. Dec 14, 2009

### 1/2"

Re: Triangle

Ok!! So now I understand!!
Thank you very much Mark44!!!

9. Dec 14, 2009

### Staff: Mentor

Re: Triangle

You're welcome!