Exercise 25 Page 312

To see whether the triangles $△ABC$ and $△XYZ$ are congruent or not, let's find the lengths of the sides.

Since we know the coordinates of the vertices, we can use the Distance Formula. Let's start with finding $AB.$ We can find the lengths of the other sides in a similar way. Before we find the lengths, notice that the exercise asks about the congruence in a specific order. This means that we need to check the lengths between the corresponding sides to see if each segment is congruent.

Corresponding Sides	Distance Formula	Result
$\overline{AB}$ and $\overline{XY}$	$\sqrt{(3-3{)}^2+(7-(\text{-}1){)}^2}\stackrel{?}{=}\sqrt{(\text{-}7-(\text{-}7){)}^2+(4-0{)}^2}$	$8\ne 4$
$\overline{BC}$ and $\overline{YZ}$	$\sqrt{(7-3{)}^2+(7-7{)}^2}\stackrel{?}{=}\sqrt{(1-(\text{-}7){)}^2+(4-4{)}^2}$	$4\ne 8$
$\overline{CA}$ and $\overline{ZX}$	$\sqrt{(3-7{)}^2+(\text{-}1-7{)}^2}\stackrel{?}{=}\sqrt{(\text{-}7-1{)}^2+(4-0{)}^2}$	$\sqrt{80}=\sqrt{80}$

Since not all of the side lengths of $△ABC$ match all of the side lengths of $△XYZ,$ the triangles are not congruent.