prove the theorem

[JayJay06]

I'm asked to prove the theorem given below, using the figure. What specifically do you need to prove in the figure?

The median drawn to the hypotenuse of a right triamgle didives it into two isosceles triangles.

 

[pka]

You need to prove that the length of AD equals the length of DC.

 

[stapel]

What specifically do you need to prove in the figure?

The median drawn to the hypotenuse of a right triamgle didives it into two isosceles triangles.

You need to prove exactly what it tells you to prove. The median AD clearly divides triangle ABC into two smaller triangles, namely triangle ADC and triangle ABD. You need to prove that triangle ADC is isosceles and that triangle ABD is isosceles.

One way to start might be to work from similarity. For instance, you could draw the altitude from D down to AC, noting that this forms a right triangle. Compare this triangle with the original triangle ABC, and see what you can conclude about angles and side lengths, etc.

Eliz.