Question

in a triangle abc ab = ac ba is produced to point d and ae bisects angle dac probe that ae is parallel to bc​

Answer 1

Answer:

Here's your answer.........

Step-by-step explanation:

Draw the tri ABC as shown in the figure below.

Now,

Ang. B = Ang C                           ...........angles opposite to equal sides of a                              

                                                              triangle are equal.

Let <B = < C = x

and < BAC = y

therefore, using angle sum property in triangle ABC,

x + x + y = 180                          

2x + y = 180                                      .............. (1)

AE bisects < DAC

therefore, < DAE = <EAC = z

y + z + z = 180                                   ................angles on a line

2z + y = 180                                      ................. (2)

now equate (1) and (2)

2x + y = 2z + y

now cancel out y from both sides

therefore,

2x = 2z

x = z

therefore, <ACB = <EAC

interior alternate angles are equal so lines are parallel.

AE || BC

hence proved.

Hope this helps.... : )