Question

In triangle pqr a and d are two points on qr such that qa=rd. If ab is parallel to pr and cd parallel to pq prove that abcd is a trapizium

Answer 1

Answer:

ABCD is a trapezium

Step-by-step explanation:

In triangle pqr a and d are two points on qr such that qa=rd. If ab is parallel to pr and cd parallel to pq prove that abcd is a trapizium

in Δ ABQ & Δ RPQ

ab || PQ

=> Δ ABQ ≅Δ RPQ

=> AB/RP  = AQ/RQ = BQ/PQ

Similalrly

in Δ CDR ≅Δ PQR

=> CD/PQ = DR/RQ  = CR/PR

AQ/RQ = DR/RQ  ( as QA = RD)

=> AB/RP  = AQ/RQ = BQ/PQ = CD/PQ = DR/RQ  = CR/PR

=> BQ/PQ = CR/PR

=> 1 -  BQ/PQ = 1 - CR/PR

=> (PQ - BQ)/PQ = (PR - CR)/PR

=> PB/PQ = PC/PR

=> ΔPBC ≅ ΔPQR

=> BC || QR

as A & D are on QR

=> BC ║ AD

hence ABCD is a trapezium