Question

Let abc be a triangle and d and e be two points on side ab such that ad= be . If dp||BC and eq|| AC , then prove that pq || ab . .............

Answer 1

Given
In triangle ABC D and E are two points on AB and DP is parallel to BC and EQ is parallel to AC

To prove
PQ parallel to AB

Answer 2

Heya friend,



Here is your answer,

Given: ABC is a triangle such that AD = BE Also DP ll BC and EQ ll AC

Prove that: PQ ll AB

Proof:

In the triangles 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 triangle(ADP) is congruent to triangle(EBQ).

Thus,

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

=> And PD ll 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.