Exercise 44 Page 605

To determine whether the triangles △ JKL and △ XYZ are congruent or not, let's find the length of the sides.

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

Corresponding Segments	Lengths	Congruent?
JK XY	sqrt((0-(-1))^2+(6-(-1))^2)=5sqrt(2) sqrt((5-3)^2+(3-1)^2)=2sqrt(2)	No *
KL YZ	sqrt((2-0)^2+(3-6)^2)=sqrt(13) sqrt((8-5)^2+(1-3)^2)=sqrt(13)	Yes ✓
JL XZ	sqrt(2-(-1))^2+(3-(-1))^2)=5 sqrt((8-3)^2+(1-1)^2)=5	Yes ✓

Since one of the side lengths of triangle △ JKL does not match the corresponding side length of triangle △ XYZ, the triangles are not congruent. △ JKL≆△ XYZ