Chapter 7.7, Problem 43SPR

To determine

To find whether $△JKL\cong △XYZ$ .

Answer to Problem 43SPR

Yes, the triangles are similar.

Explanation of Solution

Given:

The given points are-

  $J(3,9),K(4,6),L(1,5),X(1,7),Y(2,4),Z(-1,3)$ .

Calculation:

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

  $\begin{array}{l}JK=\sqrt{1^2+3^2}=\sqrt{10}\\ XY=\sqrt{1^2+3^2}=\sqrt{10}\\ \\ KL=\sqrt{3^2+1^2}=\sqrt{10}\\ YZ=\sqrt{3^2+1^2}=\sqrt{10}\\ \\ JL=\sqrt{2^2+4^2}=\sqrt{20}=2\sqrt{5}\\ XZ=\sqrt{2^2+4^2}=\sqrt{20}=2\sqrt{5}\end{array}$

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

  $\frac{JK}{XY}=\frac{KL}{YZ}=\frac{JL}{YZ}$

Therefore the triangles are similar by SSS criterion.