Chapter 5.6, Problem 5CYU

a.

To determine

Find the pairs of segments that are congruent.

Answer to Problem 5CYU

  $\overline{AB}\cong \overline{DE}and\overline{AC}\cong \overline{DF}$

Explanation of Solution

Given information:

The position of the swing depends upon the push of the swing.

  

Calculation:

  $\begin{array}{l}Now,\\ Theheightoftheswingisfixedsoonehas:\\ \overline{AB}\cong \overline{DE}\\ Thelengthofthechinisfixedsoonehas:\\ \overline{AC}\cong \overline{DF}\end{array}$

Hence, the required answer is $\overline{AB}\cong \overline{DE}and\overline{AC}\cong \overline{DF}$ .

b.

To determine

Find if the measure of $\angle A$ is greater than the measure of $\angle D$ .

Answer to Problem 5CYU

  $\angle Disgreater$

Explanation of Solution

Given information:

The position of the swing depends upon the push of the swing.

  

Calculation:

Here, we will consider $\Delta ABCand\Delta DEF$ .

Now, $\overline{AB}\cong \overline{DE}and\overline{AC}\cong \overline{DF}$

  $\begin{array}{l}BC<EF\left(given\right)\\ m\angle D>m\angle A\left(Byconverseofhingetheorem\right)\\ \therefore \angle Disgreater.\end{array}$

Hence, $\angle Disgreater$ .