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Chapter 5: Q2 (page 169)

For the following figure, if WR炉鈯�CE炉then name all angles congruent to 鈭�RCE.

Short Answer

Expert verified

The angles are congruent to 鈭�RCE is 鈭�ECW,鈭�WEC .

Step by step solution

01

Step 1. Check the figure.

Consider the figure 鈻�CREW.

02

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.

03

Step 3. Step description.

Here, CREWis a parallelogram.

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�ECW=鈭�WEC.

04

Step 4. Step description.

From the figure, WE and CE is transversal thus alternate angles are equal such that 鈭�RCE=鈭�WEC.

Therefore, the angles congruent to 鈭�RCEare 鈭�ECW,鈭�WEC.

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Most popular questions from this chapter

Quadrilateral ABCD is a parallelogram. Name the principal theorem or definition that justifies the statement.

AX=12AC

Prove Theorem 5-1.

For the following figure, if WR炉鈯�CE炉then name all segments congruent to WE炉.

Each figure in Exercises 19-24 is a parallelogram with its diagonals drawn. Find the values of x and y.

Study the markings on each figure and decide whether ABCD must be a parallelogram. If the answer is yes, state the definition or theorem that applies.
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