Question

1. use a calculator to find a rational approximation to the nearest tenth. -√86
2. in the figure below, wx≅zy and ∠wxy≅∠zyx. give the reasons for the following statement.

△wxy≅△zyx
reason:

Explanation:

Step1: Calculate square - root value

Use a calculator to find $\sqrt{86}$. $\sqrt{86}\approx9.2736$.

Step2: Apply negative sign

Since we want $-\sqrt{86}$, then $-\sqrt{86}\approx - 9.3$.

Step3: Analyze triangle congruence

We are given $\overline{WX}\cong\overline{ZY}$ (a pair of corresponding sides are equal) and $\angle WXY\cong\angle ZYX$ (a pair of corresponding angles are equal). Also, $\overline{XY}$ is common to both $\triangle WXY$ and $\triangle ZYX$, so $\overline{XY}\cong\overline{XY}$ (reflexive property of congruence). By the Side - Angle - Side (SAS) congruence postulate, if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. In $\triangle WXY$ and $\triangle ZYX$, side $\overline{WX}$ = side $\overline{ZY}$, $\angle WXY=\angle ZYX$, and side $\overline{XY}$ is common.

Answer:

1. $-9.3$
2. Side - Angle - Side (SAS) congruence postulate