Chapter 6, Problem 10CUR

To determine

To prove: the angle $AD>BE$ with the help of given information.

Answer to Problem 10CUR

The inequality $AD>BE$ has been proved.

Explanation of Solution

Given information:

The system information is:

  $m\angle B>m\angle A$

  $m\angle E>m\angle D$

Proof:

Consider the statement;$m\angle B>m\angle A$

  $m\angle E>m\angle D$

In a triangle the length of a side is proportional to the magnitude of the angle opposite to the given side.

From the figure, since $m\angle B>m\angle A$

By the property the side opposite to the greater side is greater

  $AC>BC\dots \dots$

Also, since $m\angle E>m\angle D$

By the property the side opposite to the greater side is greater

  $CD>CE\cdots \cdots (2)$

Add these two inequalities,

  $\begin{array}{c}AC+CD>BC+CE\\ AD>BE\end{array}$

Thus the inequality $AD>BE$ has been proved.