Question

$\overline{WX}$and $\overline{YZ}$are perpendicular bisectors of each other.

How many pairs of congruent triangles are shown in the diagram?

Short answer

There aresix pairs of congruent triangles.

Step-by-step solution

Step 1.  Define Perpendicular Bisector

A perpendicular bisector of a segment is a line or a ray or a segment that is perpendicular to the segment and passes through its midpoint.

Step 2.  State the theorem used 

Theorem: If a point lies on the perpendicular bisector of a segment, then the point is equidistant from the endpoints of the segment.

Step 3.  Write the pairs of congruent triangles 

In the below diagram, let the point of intersection o two perpendicular bisectors be O.

Then the pairs of congruent triangles are – $\Delta YOW\cong \Delta YOX$, $\Delta YOW\cong \Delta ZOX$, $\Delta YOW\cong \Delta ZOW$, $\Delta YOX\cong \Delta ZOX$, $\Delta YOX\cong \Delta ZOW$and $\Delta ZOX\cong \Delta ZOW$.

Therefore, there are six pairs of congruent triangles.