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Chapter 5: Q4 (page 169)

For the following figure, if RE=EWthen name all angles congruent to 鈭�ERW.

Short Answer

Expert verified

The angles are congruent to 鈭�ERWis 鈭�CRW,鈭�EWR.

Step by step solution

01

Step 1. Check the figure.

Consider the figure 鈻�CREW.

02

Step 2. Apply the concept of a parallelogram.

In a parallelogram, if the diagonals of a parallelogram are perpendicular then it is a rhombus.

In a rhombus, all sides are equal.

03

Step 3. Step description.

Here, CREW is a parallelogram then the equations are as follows:

CW=RERE=WE

Conclude from the above equation as follows:

CW=WE

Since WR鈯�CEthus the parallelogram becomes a rhombus.

As all sides are equal in a rhombus thus the sides are as follows:

RC=CW=WE=RE

This triangle is an Isosceles triangle and in the Isosceles triangle, the base angle is equal then 鈭�ERW=鈭�EWR.

04

Step 4. Step description.

From the figure, WE and RW is transversal thus alternate angles are equal such that 鈭�CRW=鈭�EWR.

Therefore, the angles congruent to 鈭�ERWare 鈭�CRW,鈭�EWR.

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