In △ABC, PQ is a line segment intersecting AB at P and AC at Q such that segPQ∥segBC. If PQ divides △ABC into two equal parts means equal in area, find BPAB
Given: △ABC, PQ∥BC
In △APQ and △ABC
∠PAQ=∠BAC (Common angle)
∠APQ=∠ABC (Corresponding angles)
∠AQP=∠ACB (Corresponding angles)
Therefore, △APQ∼△ABC (AAA rule)
hence, A(△APQ)A(△ABC)=AP2AB2
12=AP2AB2
1√2−1=APAB−1
1−√2√2=AP−ABAB
√2−1√2=BPAB