Chapter 4, Problem 4PST

To determine

To explain:

Correct triangle congruence from the given lists.

Answer to Problem 4PST

Option H is correct i.e. $△\mathrm{W}\mathrm{X}\mathrm{Y}\cong △\mathrm{J}\mathrm{K}\mathrm{I}$ .

Explanation of Solution

Given information:

  

F. $△\mathrm{W}\mathrm{X}\mathrm{Y}\cong △\mathrm{K}\mathrm{I}\mathrm{J}$

G. $△\mathrm{W}\mathrm{X}\mathrm{Y}\cong △\mathrm{I}\mathrm{J}\mathrm{K}$

H. $△\mathrm{W}\mathrm{X}\mathrm{Y}\cong △\mathrm{J}\mathrm{K}\mathrm{I}$

J. $△\mathrm{W}\mathrm{X}\mathrm{Y}\cong △\mathrm{I}\mathrm{J}\mathrm{K}$

It is given that

  $\begin{array}{l}△\overline{\mathrm{W}\mathrm{X}}\cong △\overline{\mathrm{J}\mathrm{K}}\\ \overline{\mathrm{Y}\mathrm{X}}\cong △\overline{\mathrm{I}\mathrm{K}}\\ \angle \mathrm{X}\cong \angle \mathrm{K}\end{array}$

So from the SAS ( side angle side ) triangle of congruent theorem it is observed that given two triangles have two sides and one angle is equal.

Thus, $△\mathrm{W}\mathrm{X}\mathrm{Y}\cong △\mathrm{J}\mathrm{K}\mathrm{I}$ satisfies the Correct triangle congruence theorem.