Question

pls solve Q7..figure 4. D and E are two points on AB s.t AD=BE.if DP|| BC and EQ||AC, then prove that PQ || AB​

Answer 1

Step-by-step explanation:

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)