Given △abc, ab=ac, p is interior of △abc, pc> pb prove: m∠pca> m∠pba

Proof is below.

Step-by-step explanation:

If two sides are equal, then angles opposite to them are also equal.

The angle opposite to the greater side is greater than the angle opposite to lesser side.

Given:

In ,

AB = AC

PC > PB

As sides AB = AC,

∴

As PC > PB, then, from the theorem of greater angle lies opposite to the greater side,

∴

Let

So, angle PBA is,

Angle PCA is,

Now, we have,

Multiply by -1 both sides. This changes the inequality sign.

⇒

Adding on both sides, we get

But, and .

∴ . Hence, it is proved.