Chapter 6.5, Problem 4CE

To determine

To name: the theorem that supports the deduction.

Answer to Problem 4CE

Side-Angle-Side inequality,

Explanation of Solution

Given information:

Given figure,

$\angle 1$ is a right angle; $\angle 2$ is an obtuse $\angle$ .

Calculation:

Consider the following data:

  $\overline{AC}\cong \overline{DF}$

And,

  $\overline{AB}\cong \overline{DE}$

Also $m\angle 1$ is right angle and $m\angle 2$ is obtuse angle,

That is, $m\angle 1<m\angle 2$

Then applying Side-Angle-Side Inequality,

Therefore, it is concluded that,

  $\overline{BC}>\overline{EF}$