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

XS ZS

Explanation:

Answer 2

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

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`