Chapter 1, Problem 6RP

a.

To determine

Two given angles are not congruent

Answer to Problem 6RP

  $\angle 1\text{ \& }\angle 2$ are not congruent

Explanation of Solution

Given information:

  $\angle \text{EFG is obtuse angle and }\angle \text{HJK is right angle}$

Formula used: Congruency means same size and same shape

Proof:

Since $\angle 1\ne \angle 2$

Thus, they are not congruent (By definition)

Hence Proved

b.

To determine

The congruency of two given angles

Answer to Problem 6RP

  $\text{Angles 1 and 2 are congruent, i}\text{.e}\text{., }\angle 1\cong \angle 2$

Explanation of Solution

Given information:

  $\text{Given angles }\angle \text{EFG and }\angle \text{HJK are congruent, i}\text{.e}\text{., }\angle \text{EFG }\cong \angle \text{HJK}$

Formula used: Congruency means same size and same shape.

Proof:

Since, given $\angle \text{EFG }$ and $\angle \text{HJK}$ are congruent

Then they will be also equal, by definition of congruency

  $\angle \text{EFG }\cong \angle \text{HJK}$ (Given)

  $\Rightarrow \angle \text{EFG}=\angle \text{HJK}$

  $\begin{array}{l}\Rightarrow \angle 1+20°\text{ =}\angle 2+20°\\ \left(\because \text{From the diagram: }\angle \text{EFG = }\angle \text{1+20}°\text{and }\angle \text{HJK=}\angle 2+20°\right)\\ \Rightarrow \angle 1\text{ =}\angle 2\end{array}$

  $\therefore$ When $\angle 1\text{ =}\angle 2$ , then

Yes, $\angle 1\cong \angle 2$