# Thread: Proving Right-Angled/Right Angle Triangle Help

1. ## Proving Right-Angled/Right Angle Triangle Help

Hello there,

I'm new here so please do not be angered if I make something wrong or I annoy you somehow with my question but I have just been given this question I cannot solve myself.

ABC is right-angled at A. Given that AD is perpendicular to BC, prove that:

AB X AD = BD x AC

2. Originally Posted by Hyeper
Hello there,

I'm new here so please do not be angered if I make something wrong or I annoy you somehow with my question but I have just been given this question I cannot solve myself.

ABC is right-angled at A. Given that AD is perpendicular to BC, prove that:

AB X AD = BD x AC

1. Draw a sketch.

2. You are dealing with 2 right triangles: $\displaystyle \Delta ABC$ and $\displaystyle \Delta DBA$. Both triangles have a right angle and the angle at B in common, thus they are similar.

3. Corresponding sides are proportional:

$\displaystyle \dfrac{\overline{AC}}{\overline{AB}} = \dfrac{\overline{AD}}{\overline{BD}}$

4. Multiply the equation by the two denominators.

3. Originally Posted by earboth
1. Draw a sketch.

2. You are dealing with 2 right triangles: $\displaystyle \Delta ABC$ and $\displaystyle \Delta DBA$. Both triangles have a right angle and the angle at B in common, thus they are similar.

3. Corresponding sides are proportional:

$\displaystyle \dfrac{\overline{AC}}{\overline{AB}} = \dfrac{\overline{AD}}{\overline{BD}}$

4. Multiply the equation by the two denominators.
Thank you so much for your help. It's just so simple but I failed to comprehend what the question want...

Btw, is it okay if I ask another question in this same thread or I have to start a new thread?

Thank You

4. Originally Posted by Hyeper
Thank you so much for your help. It's just so simple but I failed to comprehend what the question want...

Btw, is it okay if I ask another question in this same thread or I have to start a new thread?

Thank You
You are welcome!

Better start a new thread as it is demanded in the rules of the forum (which you have read thoroughly, of course! )