Chapter 5.6, Problem 5CYP

To determine

To prove:The angle $m\angle 1$ is greater than $m\angle 2$ .

Explanation of Solution

Given information:

The given geometry is

  

The sides $JN>NM$

  $\overline{NK}$ is a median of $\Delta JMN$ .

Formula Used:

Hinge theorem is

If two sides of a triangle correspond to two sides of another triangle, and the angle of inclination of the first triangle is greater than the angle of inclination of the second triangle, so the sides of the first triangle are longer than the sides of the third side of the second triangle.

Prove:

It is given thatthe sides $JN>NM$

Thus, by Hinge theorem $m\angle JKN>m\angle MKN$

Since, $m\angle JKN=m\angle 1$ and $m\angle MKN=m\angle 2$ .

Substitute the values.

  $m\angle 1>m\angle 2$

Hence, proved.