Question

In trapezium PQRS side PQ|| side SR,AR= 5 AP, AS= 5 AQ then prove that SR=5 PQ​

Answer 1

Answer:

Given

side PQ || side SR

AR = 5 AP

AS = 5 AQ

To prove : SR = 5 PQ

Proof : In ΔAPQ and ΔARS

∠PAQ=∠RAS (Vertically opposite angles) ∠PAQ=∠RSA (Alternate angles , side PQ || side SR and QS is a transversal line)

By AA test of similarity

ΔAPQ∼ΔARS

SR

PQ

=

AR

AP

(Corresponding side are proportional)

⇒

SR

PQ

=

5

1

(AR=5AP)

⇒SR=5PQ

Hence proved.