Chapter 13.8, Problem 13WE

To determine

To prove $e=c\text{ and d=a-b}$

Explanation of Solution

Given information :  $HOJK$ is an isosceles trapezoid with coordinates represented in figure

  

Concept used:

Trapezoid has one pair of opposite sides is parallel. In isosceles trapezoid one pair of opposite sides is parallel.

Explanation:  Vertex O of triangle is at origin so it has coordinates $\left(0,0\right)$

Draw heights in given trapezoid as shown in below figure

  

To prove $e=c$ and $d=a-b$

As trapezoid $HOJK$ is isosceles so $JO=KH$

Both the heights drawn are parallel ato each other and equidistant from side JK and OH.

Therefore,

  $e=c$

From above figure distance from vertex O to H is $a$ and distance from vertex O to K is $d$

So distance $a$ can be written as $a=d+b$

On rearranging equation to find value of d

  $d=a-b$

Hence Proved

  $e=c\text{ and d=b-c}$