Question

Let ABC be a triangle and D and E be two points on side AB such that
AD=BE. IFDP || BC and EQ || AC, then prove that PQ || AB.
Can anyone tell the answer...........​

Answer 1

Answer:

Given= ABC is a triangle such that AD = BE also DP // BC and EQ // AC.

Prove that:- PQ//AB.

Proof:-

In the triangle ADP and EBQ;

=> AD= BE (given).

=> Angle (DAP) = Angle (BEQ).

[ corresponding interior angles]

=> Angle (ADP) = Angle (EBQ).

[ corresponding interior angles]

Therefore,

By, ASA congruency triangle (ADP) is congruent to triangle (EBQ).

Thus,

=> By CPCT:- PD=BQ ------(1).

=> And PD//BQ [given] ------(2).

Now,

since one pair of opposite side are equal and parallel.

Therefore, the quadrilateral DPQB is a parallelogram and PQ//DB. (hence proved ).

Hope it helps you,

Thank you.