Chapter 5.1, Problem 4WE

To determine

To calculate: the names of all angles congruent to $\angle ERW$ , If $RE=EW$ .

Answer to Problem 4WE

The angles congruent to $\angle ERW$ is;

  $\begin{array}{l}\angle ERW=\angle CRW\\ \angle ERW=\angle EWR\end{array}$

Explanation of Solution

Given information:

System figure:

  

Calculation:

Consider that the quadrilateral CREW is parallelogram.

Then,

  $CR=WE$

  $CW=RE$......(1)

It is known that $RE=WE\dots \dots$ (2)

From equation (1) and (2),

  $\begin{array}{l}WE=RC\\ =CW\\ =RE\cdots \cdots (3)\end{array}$

This parallelogram become a Rhombus

In $△REWRE=WE$ From equation (3)

This triangle is an Isosceles triangle and In Isosceles triangle base angle are equal then,

  $\angle ERW=\angle EWR\dots \dots$ (4)

The line $CR\parallel WE$ and $RW$ is a transversal then alternate angles are equal,

  $\angle CRW=\angle EWR\dots \dots (5)$

From equation (4) and (5) ,

  $\angle ERW=\angle CRW$

Therefore, the angles congruent to $\angle ERW$ is;

  $\begin{array}{l}\angle ERW=\angle CRW\\ \angle ERW=\angle EWR\end{array}$