Chapter 8.3, Problem 34E

To determine

The length of the segments.

Whether the segments are congruent or not.

The greater segment if the segments are not congruent.

Answer to Problem 34E

  $\begin{array}{l}EF=5\\ GH=6.3\end{array}$

The lengths are not same, therefore, $\overline{EF}\text{and}\overline{GH}$ are not congruent. The length of $\overline{GH}$ is greater.

Explanation of Solution

Given:

The given points are:

  $\begin{array}{l}\overline{EF}:\\ E\left(1,4\right)\\ F\left(5,1\right)\\ \overline{GH}:\\ G\left(-3,1\right)\\ H\left(1,6\right)\end{array}$

Calculation:

Line segments having the same length are called the congruent segments.

The lengths can be calculated as:

  $\begin{array}{l}EF=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ EF=\sqrt{{\left(5-1\right)}^2+{\left(1-4\right)}^2}\\ EF=\sqrt{16+9}\\ EF=\sqrt{25}\\ EF=5\\ \\ GH=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ GH=\sqrt{{\left(1-\left(-3\right)\right)}^2+{\left(6-1\right)}^2}\\ GH=\sqrt{16+25}\\ GH=\sqrt{41}\\ GH=6.3\end{array}$

The lengths are not same, therefore, $\overline{EF}\text{and}\overline{GH}$ are not congruent. The length of $\overline{GH}$ is greater.