Chapter 5.1, Problem 2WE

To determine

To calculate: the names of all angles congruent to $\angle RCE$ , If $WR\perp CE$ .

Answer to Problem 2WE

The angles congruent to $\angle RCE$ is;

  $\angle RCE=\angle ECW$

  $\angle RCE=\angle WEC$

Explanation of Solution

Given information:

System figure:

  

Calculation:

Consider that the quadrilateral CREW is parallelogram.

In the given figure,

If $WR\perp CE$ This parallelogram become a Rhombus

In a Rhombus all side are equal.

  $\begin{array}{l}RC=CW\\ =WE\dots \dots (1)\\ =RE\end{array}$

  $\ln \text{Δ}CWO,CW=WE$

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

  $\angle ECW=\angle WEC\dots \dots$ ( 2 )

  $\text{CR}\parallel \text{WE}$ and $\text{CE}$ is a transversal then alternate angles are equal,

  $\angle RCE=\angle WEC\cdots \cdots$ ( 3 ),

From equation ( 2 ) and ( 3 ),

  $\angle RCE=\angle ECW$

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

  $\angle RCE=\angle ECW$

  $\angle RCE=\angle WEC$