Question

in the given figure AE bisects angle CAD
and angle B =angle C
prove that AE parallel BC
​

Answer 1

Step-by-step explanation:

2angle EAC =DAC (angle is bisected)

=angle B +angle C (exterior angle prpty)

therefore 2angle EAC =2 angle c (angle c = b)

hence angleEAC= angle C

SINCE alternate angles are equal Ae Paralle to Bc

HENCE PROVED

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Answer 2

Answer:

As, ∠CAD is bisected by AE

∠CAD = 2∠CAE - 2∠DAE ..........(1)

Now, using the property, “an exterior angle of a triangle in equal to the sum of the two opposite interior angles”, we get,

∠CAD ∠B +∠C

∠CAD = 2∠C (∠B = ∠C)

2∠CAE = 2∠C (using 1)

∠CAE = ∠C

∠CAE = ∠ACB

Hence, using the property, if alternate interior angles are equal, then the two lines are parallel, we get,

∠CAE = ∠ACB

Thus,AE || BC

Hence proved.