Question

The bisectors of angles P and Q of a triangle PQR meet the opposite sides at B and A respectively. If AB is parallel to PQ , prove that triangle PQR is isosceles
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Answer 1

Given, the bisector of the angles B and C of a triangle ABC meet the opposite sides in D and E respectively.

Again, we can show that BE = CD

Now, in Δ BEC and Δ CDB

BE = CD {by proof}

BC = CB {common}

So, by RHS congruence,

Δ BCE ≅ Δ CDB

By CPCT, we get

∠BCE = ∠CBD

Now, AB = AC {sides opposite to equal angles of a triangle are equal}

Hence, Δ ABC is an isoscel