# Thread: Proving the congruency of two triangles in a parallelogram.

1. ## Proving the congruency of two triangles in a parallelogram.

ABCD is a parallelogram and P is a point on the diagonal AC. Prove that triangle ABP and APD have the same area.
How do I prove this?
The attachment is a picture of a parallelogram that is drawn. Please use theorem to prove this, thank you.
Whoever solve this will save my life.

2. Originally Posted by RoyJones
ABCD is a parallelogram and P is a point on the diagonal AC. Prove that triangle ABP and APD have the same area.
How do I prove this?
The attachment is a picture of a parallelogram that is drawn. Please use theorem to prove this, thank you.
Whoever solve this will save my life.
1. The diagonal AC divides the parallelogram into 2 congruent triangles. Since these two triangles have the same base (= AC) the distances of the parallels to the diagonal must be equal.

2. Therefore the triangles APB and ADP have the same height and the same base AP. Thus the areas must be equal.

3. Great solution!

4. Originally Posted by Also sprach Zarathustra
Great solution!
How simple it is when you know the fundamentals.Thanks earboth