Question

YS is the perpendicular bisector of XYZ and YS is a shared side of XYS and ZYS. which of the following must be congrent in order to verify that XYS= ZYS?

Answer 1

Answer:

The triangles SYX and SYZ are congrient so by CPCTC $XY\cong YZ$, $XS\cong ZS$ and $\angle X\cong \angle Z$.

Step-by-step explanation:

Given information: YS is the perpendicular bisector of XYZ.

In triangle YXS and triangle YSZ,

$\angle SYX=\angle SYZ$                 (YS is the perpendicular bisector of XYZ)

$YS=YS$                                            (Common side, Reflexive property)

$\angle YSX=\angle YSZ=90^{\circ}$   (YS is the perpendicular bisector of XYZ)

By ASA postulate,

$\triangle SYX\cong \angle SYZ$

The corresponding parts of congruent triangles are congruent. so,

$XY\cong YZ$

$XS\cong ZS$

$\angle X\cong \angle Z$