Question

how to show that: line segments joining the mid pints of two sides of a triangle is parallel to the third side​

Answer 1

Given: In triangle ABC,point P nd Q r the midpoint of seg AB nd Seg AC,

Prove:

PQ is parallel to BC

proof:

in triangle APQ nd traingle PQB,

area traingle APQ/area traingle PQB= AP/PB.. (1)(area proportional 2 height)

NOW,

area traingle APQ/area triangle PQC= AQ/ QC.....(2)(area proportional 2 height)

therefore,

seg PQ is the common base nd area traingle PQB=area traingle PQC....(3)

therefore,

AP/PB= AQ/QC..from (1 &2&3)

seg PQ is parellel to seg BC