Chapter 5: Q2 (page 169)

For the following figure, if $\bar{W R} ⊥ \bar{C E}$ then name all angles congruent to $∠ R C E$ .

Short Answer

Expert verified

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

Step by step solution

Step 1. Check the figure.

Consider the figure $▱ C R E W$ .

Step 2. Apply the concept of the 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, $C R E W$ is a parallelogram.

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 $∠ E C W = ∠ W E C$ .

Step 4. Step description.

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

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

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For the following figure, if $\bar{W R} ⊥ \bar{C E}$ then name all angles congruent to $∠ R C E$ .

Short Answer

Step by step solution

Step 1. Check the figure.

Step 2. Apply the concept of the parallelogram.

Step 3. Step description.

Step 4. Step description.

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For the following figure, if WR¯⊥CE¯then name all angles congruent to ∠RCE.

Short Answer

Step by step solution

Step 1. Check the figure.

Step 2. Apply the concept of the parallelogram.

Step 3. Step description.

Step 4. Step description.

One App. One Place for Learning.

Most popular questions from this chapter

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For the following figure, if $\bar{W R} ⊥ \bar{C E}$ then name all angles congruent to $∠ R C E$ .