In the diagram, O is the centre of two concentric circles. X and Y lie on the circumference of the smaller circle, while W and Z lie on the circumference of the larger circle. WY and XZ intersect at O. With clear reasoning, prove that triangle WOX and triangle ZOY are congruent. Answer ... ...

1. Identify one pair of equal corresponding sides from the larger circle.

Since $W$ and $Z$ lie on the circumference of the larger circle with centre $O$,

$OW = OZ$.

These are radii of the same circle.

2. Identify another pair of equal corresponding sides from the smaller circle.

Since $X$ and $Y$ lie on the circumference of the smaller circle with centre $O$,

$OX = OY$.

These are radii of the same circle.

3. Use the equal included angle and conclude congruence.

Lines $WY$ and $XZ$ intersect at $O$, so

$\angle WOX = \angle ZOY$

because vertically opposite angles are equal.

Hence, $\triangle WOX \cong \triangle ZOY$ by SAS.