Question

help me in solving 26part (help in drawing figure)

Answer 1

Refer the attachment for figure.



Here we are given that

AB = AC

=> angle ABC = angle ACB

Let angle ABC be x

=> angle ABC = angle ACB = x


Now by exterior angle property,

angle ABC + angle ACB = angle DAC

=> angle DAC = x + x

=> angle DAC = 2x

Given that angle DAC is bisected by AE

=> angle EAC = angle DAC/2

=> angle EAC = 2x/2

=> angle EAC = x

and angle EAB = angle EAC + angle A

=> angle EAB = x + angle A


Now, again by exterior angle property

angle ABG = angle A + angle ACB

=> angle ABG = angle A + x


But angle EAB is also = angle A + x

=> angle EAB = angle ABG.


Now, angle EAB and angle ABG are alternate angles and they are equal.


"If the Alternate angles formed by the transversal, intersecting two lines are equal, then the two lines are parallel"


=> AE || BC


Hence Proved :)