Question

in the figure AE bisect angle BAD and Af bisect angle CAD and AE parell to Af show that B,A,C are collinear

Answer 1

Yes B,A,C is Collinear


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Answer 2

Answer:

Given : AE and AF are the angle bisectors of angle BAD and angle CAD respectively,

Such that, AE ⊥ AF

To prove : B, A, C are co-linear.

Proof:

By the property of angle bisector,

m∠DAE = m∠EAB

And, m∠DAF = m∠FAC,

Since, AE ⊥ AF

⇒ m∠FAE = 90°

⇒ m∠DAF + m∠DAE = 90°

By multiplying 2 on both sides,

⇒ 2 ( m∠DAF + m∠DAE) = 180°

⇒ m∠DAF + m∠DAF + m∠DAE + m∠DAE = 180°

⇒  m∠DAF + m∠EAB + m∠DAE + m∠FAC = 180°

⇒ m∠CAB = 180°

⇒ B, A, C are co-linear,

Hence, proved.