Chapter 4.3, Problem 37HP

To determine

To explain:

  $△CAB\cong △ZYX$ said by jasmine and $△ABC\cong △YXZ$ said by will is correct or not.

Answer to Problem 37HP

  $△CAB\cong △ZYX$ said by jasmine and $△ABC\cong △YXZ$ said by will is correct.

Explanation of Solution

Given information:

  

Observe the sides,

  $\overline{AC}\cong \overline{YZ}$ because they have the same length $0.9$ .

  $\overline{AB}\cong \overline{YX}$ , because they have same length $1$ .

  $\overline{BC}\cong \overline{XZ}$ , because they have the same length $1.5$ .

Thus,

  $\angle A$ corresponds with $\angle Y$ , as they are opposite to a pair of congruent sides $\overline{BC}\cong \overline{XZ}$ .

  $\angle B$ corresponds with $\angle X$ , as they are opposite to a pair of congruent sides $\overline{AC}\cong \overline{YZ}$ .

  $\angle C$ corresponds with $\angle Z$ , as they are opposite to a pair of congruent sides $\overline{AB}\cong \overline{YX}$

Therefore, $△ABC\cong △YXZ$ because corresponding vertices are placed in the same location.

Also, $△CAB\cong △ZYX$ because corresponding vertices are placed in the same location.

Hence, both of them correct.