Asapin △mnp, point q is on side mn so that pm=pq. prove that pn> pm.

Given: In , Point Q is on the side MN so that PM=PQ.

Isosceles Triangle states:

* A triangle with two equal sides.

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

Since, PQ=PM

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:

To prove PN>PM.

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     hence Proved!

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step-by-step explanation:

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