Question

In Fig 7.55, the sides AC and BC of a A ABC are produced such
that
AC = CQ and BC = CP.
Prove that PQ || AB and PQ = AB.
(Hint: Prove that A ABC = A QPC.​

Answer 1

Step-by-step explanation:

Given :

• AC = CQ
• BC = CP

To prove :

• PQ || AB

• PQ = AB

Lets consider ΔABC and ΔPQC

1. AC = CQ (given)
2. BC = CP (given)
3. ∠PCQ = ∠ACB

∴ By SAS criterion, ΔABC ≅ ΔPQC

∴ By CPCT, PQ = AB, and ∠QPC = ∠ABC

Since ∠QPC = ∠ABC, meaning alternate interior angles are equal

we can say that PQ||AB

∴ Proved

Hope it helped!