In triangle ABC, P and Q are points on the sides AB and AC respectively such that PQ is parallel - Maths - Triangles

Question

In triangle ABC, P and Q are points on the sides AB and AC
respectively such that PQ is parallel to BC Prove that medium AD,
drawn from A to BC, bisects PQ

Utkarsh Singh · Accepted Answer

Given - triangle ABC
PQ is parallel to BC
AD is median of BC ----> BD = CD
To prove - AD bisects PQ
Let us assume that the opint of intersection of AD and PQ is
O
-----> we need to prove PO = QO
In triangle APQ and triangle ABC
∠PAQ = ∠ BAC (∠A is
common)
∠APQ = ∠ABC (corresponding
angles)
therefore, by AAA similarity criteria,
triangle APQ ~ triangle ABC
----> PQ is similar to BC BC (sides of similar triangles are
proportional)
-----> if median AD bisects BC, it should bisect PQ too
-----> PO = QO
hope this is the correct answer plz comment if not!!!!

In triangle ABC, P and Q are points on the sides AB and AC respectively such that PQ is parallel to BC. Prove that medium AD, drawn from A to BC, bisects PQ.