Based only on the given information, it is guaranteed that wy xz .

In the given figure in the two triangles ZWX and ZYX ,the sides given equal are

ZW=ZY,

WX=YX,

XZ=XZ.

The three sides of both triangles are equal ,so  the triangles are congruent by SSS congruence.In congruent by C.P.C.T the three angles are equal.

So we can say <ZXW=<ZXY.

These are angles made on a straight line so <ZXW=<ZXY =90 degrees.

By definition of perpendicular lines WY ⊥ XZ.

Option A  .True.

True

Step-by-step explanation:

Given: In ΔWYZ, ZW≅ZY, WX≅YX and XZ≅XZ.

To prove: WY⊥XZ

Proof:

From ΔWXZ and ΔYXZ, we have

ZW≅ZY (Given)

WX≅YX (Given)

and XZ≅XZ (Common)

Thus, By SSS rule, ΔWXZ ≅ ΔYXZ.

therefore, by CPCTC, ∠ZXW=∠ZXY

Now, since, these angles are made on straight line, therefore ∠ZXW=∠ZXY=90°

Thus, WY⊥XZ is guaranteed true.

Hence proved.