Question
Tue September 25, 2012 By:

# Is Basic Proportionality Theorem only applicable for triangles

Expert Reply
Tue September 25, 2012
You can apply basic proportionality theorem and its converse in triangle only. However on the basis of this concept, you can do some proof for other figures such as parallelograms, quadrilaterals etc.
nFor example, consider that you are given with the following question as
ABCD as a parallelogram such that P and Q are two points on AB and DC. If AP: PB = 2:3 and PQ || BC and then show that DQ: QC = 2:3.
tYou can prove it by drawing diagonal AC and mark the point G where AC and PQ intersect.

Since PQ || BC so, PG || BC.

Now, PG || BC and AP: PB = 2:3.

So, by using converse of BPT, AG: GC= 2:3.

Now, in triangle ACD, AD || GQ and AG: GC= 2:3.

So, by using converse of BPT, DQ: QC= 2:3

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# P and Q are the points on the side CA and CB of a triangle ABC , right angled at C . prove that (AQ)square + (PB)square = (AB)square + (PQ)square .

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