Asap (6 points each) in △abc, point d is on side ab so that ca=cd. prove that bc> ac.

Given: In , point D is on the side AB so that CA=CD.

Isosceles Triangle states:

* A triangle with two equal sides.

*The angles which are opposite to the equal sides are also equal.

Since, CA=CD

By definition of isosceles triangle,

is an isosceles triangle,

All the three angles within an isosceles triangle are acute. Acute angles are always less than 90 degrees.

therefore,      ......[1]

Now, Consider ,

Exterior Angle Property state that  an exterior angle of a triangle is equal to the sum of the opposite interior angles.

Therefore, by exterior angle property in we have ;

So,

From [1] we have:

Consider ,

Sine law states that an equation relating the lengths of the sides of a triangle to the sines of its angles.

Now, using Sine law in  ,

     ......[2]

Since,

so,                           ......[3]

From [2] and [3] we have;

or we can write it as     hence Proved!

the answer to this question is yes