Question

in angle ABC p and q are points on AB andAC respectively such that PB=QC and PQ parallel BC prove that the triangle is isosceles

Answer 1

Given: ABC is a triangle and P and Q are point on AB and AC.
PQ ll BC .
To Prove: ABC is an isosceles triangle.
Proof: In triangle ABC
PQ ll BC
since, AP/ PB= AQ/QC. ( by converse
thales theorem)

AP/PB =AQ /PB ( given, PB =QC)
=> AP =AQ
since, a triangle in which two sides are equal is an isosceles triangle. ( Proved)