Question

In △ABC, AB ≅ AC. Ray AD is the bisector of exterior
angle EAC. Prove that AD || BC.

Answer 1

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Answer 2

Answer:

opposite sides are parallel. ABCD is a parallelogram.

Step-by-step explanation:

AD bisects ∠PAC, then

∠PAD=∠DAC=

2

1

∠PAC→(1)

Also AB=AC

∴∠BCA=∠ABC→(2)

In △ ABC, ∠PAC is an exterior angle.

∠PAC=∠ABC+∠BCA

∠PAC=∠BCA+∠BCA [from (2)]

∠PAC=2∠BCA

∠BCA=

2

1

∠PAC

∠BCA=∠DAC [from (1)]

(ii) For lines BC and AD , AC is transversal & ∠DAC &

∠BCA are alternate interior angles and are equal. Therefore BC∥AD. In ABCD, BC∥AD & AB∥CD .

Since, opposite sides are parallel. ABCD is a parallelogram.

solution