Question

question 20 of 28
ys is the perpendicular bisector of △xyz, and ys is a shared side of △xys and △zys. which of the following must be congruent in order to verify that △xys≅△zys?
a. zy≅zs
b. xs≅xy
c. xy≅ys
d. xs≅zs

Explanation:

Step1: Recall congruence postulates

We know that $\overline{YS}$ is the perpendicular bisector of $\triangle XYZ$, so $\angle YSX=\angle YSZ = 90^{\circ}$ and $\overline{YS}$ is common to both $\triangle XYS$ and $\triangle ZYS$. To prove $\triangle XYS\cong\triangle ZYS$ by the Side - Angle - Side (SAS) congruence postulate or Hypotenuse - Leg (HL) congruence postulate (if it is a right - triangle situation), we need to show that the other pair of corresponding sides are equal.

Step2: Analyze the options

In right - triangles $\triangle XYS$ and $\triangle ZYS$, if $\overline{XS}\cong\overline{ZS}$, along with $\angle YSX=\angle YSZ = 90^{\circ}$ and $\overline{YS}=\overline{YS}$ (common side), we can prove $\triangle XYS\cong\triangle ZYS$ by the SAS congruence postulate.

Answer:

D. $\overline{XS}\cong\overline{ZS}$