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

pointsStep-by-step explanation:...

Given △abc, ab=ac, p is interior of △abc, pc pb

evelynnn511

08.01.2022

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 $\Delta ABC$ ,

AB = AC

PC > PB

As sides AB = AC,

∴ $m\angle ABC=m\angle ACB=a(Let)$

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

∴ $m\angle PBC m\angle PCB$

Let $m\angle PBC =x\textrm{ and } m\angle PCB=y$

So, angle PBA is, $m\angle PBA=m\angle ABC-m\angle PBC=a-x$

Angle PCA is, $m\angle PCA=m\angle ACB-m\angle PCB=a-y$

Now, we have, x y

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

⇒ -x < -y

Adding on both sides, we get

a-x

But, $m\angle PBA=a-x$ and $m\angle PCA=a-y$ .

∴ a-x . Hence, it is proved.

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