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!

step-by-step explanation:

1. practice, practice & more practice

2. review errors

3. master the key concepts

do not try to memorise the processes.

4. understand your doubts.

5. create a distraction free study environment

6. create a mathematical dictionary

7. apply maths to real world problems.

step-by-step explanation:

there are 36 inches in a yard

25 : 36 = 0.69 yards (you can round to 0.70)