Question

ABCis an isosceles triangle In which AB=AC AD bisector exterior angle QAC and CD //BA show in the figure
(I) angleDAC
(ii) ABCD is a parallelogram ​

Answer 1

Answer:

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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.