△XYZ is an isosceles triangle such that XY=XZ. It is given that YS⊥XZ and ZT⊥XY. What is the relation between YS and ZT?

In △XYZ, it is given that XY=XZ, which means △XYZ is an isosceles triangle.
Consequently, the angles opposite to equal sides are also equal:

∠XZY=∠XYZ
Now consider △YSZ and △ZTY:

∠YSZ=∠ZTY=90
∘
(since YS⊥XZ and ZT⊥XY)

∠SZY=∠TYZ (since ∠XZY=∠XYZ)

YZ=ZY (Common side)

By Angle-Angle-Side (AAS) congruence criterion:

△YSZ≅△ZTY
By CPCT (Corresponding Parts of Congruent Triangles):

YS=ZT