Chapter 4: Q.18 (page 162)

$\bar{W X}$ and $\bar{Y Z}$ 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

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 – $Δ Y O W ≅ Δ Y O X$ , $Δ Y O W ≅ Δ Z O X$ , $Δ Y O W ≅ Δ Z O W$ , $Δ Y O X ≅ Δ Z O X$ , $Δ Y O X ≅ Δ Z O W$ and $Δ Z O X ≅ Δ Z O W$ .

Therefore, there are six pairs of congruent triangles.

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$\bar{W X}$ and $\bar{Y Z}$ are perpendicular bisectors of each other.
How many pairs of congruent triangles are shown in the diagram?

Short Answer

Step by step solution

Step 1. Define Perpendicular Bisector

Step 2. State the theorem used

Step 3. Write the pairs of congruent triangles

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WX¯and YZ¯are perpendicular bisectors of each other.How many pairs of congruent triangles are shown in the diagram?

Short Answer

Step by step solution

Step 1. Define Perpendicular Bisector

Step 2. State the theorem used

Step 3. Write the pairs of congruent triangles

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Geometry

Discrete Mathematics

Calculus

Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

$\bar{W X}$ and $\bar{Y Z}$ are perpendicular bisectors of each other.
How many pairs of congruent triangles are shown in the diagram?