Prove the angles equal to prove the sides triangle problem

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This is an mensurational problem of triangles.

Homework Statement

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.
Please help!

 

[Mark44]

This is an mensurational problem of triangles.

Homework Statement

In triangle ABC, anngleB=90degrees ,AB=(2x+1)cm.If the area and perimeter of the triangle ABC.

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.

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.
Please help!

 

[1/2"]

I am really sorrrrrry!

 

[Mark44]

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?

 

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

 

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Is there something wrong i have done??
Please be free to tell

 

[Mark44]

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

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?

 

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

 

[Mark44]

You're welcome!