91Ó°ÊÓ

The given diagram is:

It is being given that $∠W$and $∠Y$are right angles and $\stackrel{¯}{WX}â‰\dots \stackrel{¯}{YX}$.

As, $∠W$and $∠Y$are right angles, therefore, the triangles$△XWZ$ and$△XYZ$ are the right angled triangles.

In the triangles$â–³XWZ$and $â–³XYZ$, it can be noticed that the side$XZ$is common.

Therefore,$\stackrel{¯}{XZ}â‰\dots \stackrel{¯}{XZ}$ by using the reflexive property.

$\stackrel{¯}{XZ}$is the hypotenuse of the triangles $△XWZ$and $△XYZ$respectively.

As, $\stackrel{¯}{XZ}â‰\dots \stackrel{¯}{XZ}$, therefore the hypotenuses of the triangles $â–³XWZ$and $â–³XYZ$are equal.

$\stackrel{¯}{WX}$and$\stackrel{¯}{YX}$are the legs of the triangles $△XWZ$and $△XYZ$respectively.

As, $\stackrel{¯}{WX}â‰\dots \stackrel{¯}{YX}$, therefore the legs of the triangles$â–³XWZ$ and $â–³XYZ$are equal.

In the triangles$â–³XWZ$ and $â–³XYZ$, it can be noticed that role="math" localid="1649850649551" $\stackrel{¯}{WX}â‰\dots \stackrel{¯}{YX}$ and$\stackrel{¯}{XZ}â‰\dots \stackrel{¯}{XZ}$.

Therefore, the triangles$â–³XWZ$ and$â–³XYZ$ are the congruent triangles by using the HL method.

The triangles role="math" localid="1649850602993" $â–³XWZ$and$â–³XYZ$are the congruent triangles.

Therefore by using the corresponding parts of congruent triangles it can be said that $\stackrel{¯}{WZ}â‰\dots \stackrel{¯}{YZ}$.

The complete table is: