Question

Explain the B.P.T theorem

Answer 1

Given: In  ΔABC, DE is parallel to BC
Line DE intersects sides AB and PQ in points D and E, such that we get triangles A-D-E and A-E-C.
To Prove: ADBD=AECE
Construction: Join segments DC and BE
Proof: 
In ΔADE and ΔBDE,
A(ΔADE)A(ΔBDE)=ADBD                 (triangles with equal heights)
In ΔADE and ΔCDE,
A(ΔADE)A(ΔCDE)=AECE                  (triangles with equal heights)
Since ΔBDE and ΔCDE have a common base DE and have the same height we can say that,
A(ΔBDE)=A(ΔCDE)
Therefore,
A(ΔADE)A(ΔBDE)=A(ΔADE)A(ΔCDE)
Therefore,
ADBD=AECE
Hence Proved.