Question

In ∆ ABC, seg AB ≅ seg AC. Ray AF bisects ∠DAC, Ray CF ‖ ray BA. Prove that □ ABCF is a parallelogram.
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Answer 1

Given : ∆ ABC, seg AB ≅ seg AC. Ray AF bisects ∠DAC, Ray CF ‖ ray BA.

To find :  Prove that ABCF is a parallelogram

Solution:

AB = AC

=> ∠ABC = ∠ACB

∠DAC = ∠ABC + ∠ACB  ( Exterior angle of triangle = sum of opposite two interior angle )

=> ∠DAC = 2∠ABC = 2∠ACB

Ray AF bisects ∠DAC,

=> ∠DAF  = ∠CAF = (1/2)∠DAC

=>  ∠CAF =  (1/2)2∠ACB

=> ∠CAF =  ∠ACB

=> AF ║ BC

   CF ║ BA  ( given)

=> ABCF is a parallelogram

QED

Hence Proved

 

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