In the given figure, ABC is a triangle and PQ is a straight line meeting AB in P and AC in Q. If AP = 1 cm, PB = 3 cm, AQ = 1.5 cm, QC = 4.5 cm, prove that area of ΔAPQ is 1/16 of the area of ΔABC.

Question

Philoid · Accepted Answer

We have

Also ∠ A = ∠ A

So, by SAS similarity criterion ΔAPQ ~ ΔABC

We know that if two triangles are similar then the ratio of their areas is equal to the ratio of the squares of their corresponding sides.

Hence, proved.