Chapter 5: Q4 (page 169)

For the following figure, if $R E = E W$ then name all angles congruent to $∠ E R W$ .

Short Answer

Expert verified

The angles are congruent to $∠ E R W$ is $∠ C R W, ∠ E W R$ .

Step by step solution

Step 1. Check the figure.

Consider the figure $▱ C R E W$ .

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.

Step 3. Step description.

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

$\begin{array}{l} C W = R E \\ R E = W E \end{array}$

Conclude from the above equation as follows:

$C W = W E$

Since $W R ⊥ C E$ thus the parallelogram becomes a rhombus.

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

$\begin{matrix} R C = C W \\ = W E \\ = R E \end{matrix}$

This triangle is an Isosceles triangle and in the Isosceles triangle, the base angle is equal then $∠ E R W = ∠ E W R$ .

Step 4. Step description.

From the figure, WE and RW is transversal thus alternate angles are equal such that $∠ C R W = ∠ E W R$ .

Therefore, the angles congruent to $∠ E R W$ are $∠ C R W, ∠ E W R$ .

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For the following figure, if $R E = E W$ then name all angles congruent to $∠ E R W$ .

Short Answer

Step by step solution

Step 1. Check the figure.

Step 2. Apply the concept of a parallelogram.

Step 3. Step description.

Step 4. Step description.

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

Short Answer

Step by step solution

Step 1. Check the figure.

Step 2. Apply the concept of a parallelogram.

Step 3. Step description.

Step 4. Step description.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Statistics

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Applied Mathematics

Study anywhere. Anytime. Across all devices.

For the following figure, if $R E = E W$ then name all angles congruent to $∠ E R W$ .