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Chapter 4: Q.18 (page 162)

WX炉and YZ炉are perpendicular bisectors of each other.

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

Short Answer

Expert verified

There aresix pairs of congruent triangles.

Step by step solution

01

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.

02

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.

03

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 鈥� 螖YOW鈮�螖YOX, 螖YOW鈮�螖ZOX, 螖YOW鈮�螖ZOW, 螖YOX鈮�螖ZOX, 螖YOX鈮�螖ZOWand 螖ZOX鈮�螖ZOW.

Therefore, there are six pairs of congruent triangles.

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