Chapter 7.7, Problem 44SPR

To determine

To find whether $△JKL\cong △XYZ$ .

Answer to Problem 44SPR

No, the triangles are not similar.

Explanation of Solution

Given:

The given points are-

  $J(-1,-1),K(0,6),L(2,3),X(3,1),Y(5,3),Z(8,1)$ .

Calculation:

Let us find the length of the corresponding sides of both the triangles using the distance formula as follows-

  $\begin{array}{l}JK=\sqrt{1^2+7^2}=\sqrt{50}=5\sqrt{2}\\ XY=\sqrt{2^2+2^2}=\sqrt{8}=2\sqrt{2}\\ \\ KL=\sqrt{2^2+3^2}=\sqrt{13}\\ YZ=\sqrt{2^2+3^2}=\sqrt{13}\end{array}$

Now, finding out the ratio of their corresponding sides as follows-

  $\frac{JK}{XY}\ne \frac{KL}{YZ}$

Since corresponding sides are not proportional so the triangles are not similar.