Chapter 4.5, Problem 8WE

(a)

To determine

To Find: whether it is possible to prove $\angle AOB$ congruent to $\angle AOC$ shown in figure .

Answer to Problem 8WE

Yes, it is possible.

Explanation of Solution

Given:

Given figure is.

  $\begin{array}{l}AB\cong AC\\ OB\cong OC\end{array}$

Calculation:

Using two-column proof.

  $\begin{array}{cc}\text{Statements}& \text{Reasons}\\ AO=AO& \text{Common}\\ AB=AC& \text{Given}\\ \begin{array}{l}OB=OC\\ \Delta AOB\cong \Delta AOC\\ \angle AOB\cong \angle AOC\end{array}& \begin{array}{l}\text{Given}\\ \text{By SSS}\\ \text{By CPCT}\end{array}\end{array}$

Therefore, it is possible to prove $\angle AOB\cong \angle AOC$ .

(b)

To determine

To Find: whether it is possible to prove $\angle AOB\text{and }AOC$ are right angles.

Answer to Problem 8WE

No.

Explanation of Solution

Given figure is.

  $\begin{array}{l}AB\cong AC\\ OB\cong OC\end{array}$

Calculation;

It is possible to prove $\angle AOB\cong \angle AOC$ as shown below but data are insufficient to prove them right angles.

Using two-column proof.

  $\begin{array}{cc}\text{Statements}& \text{Reasons}\\ AO=AO& \text{Common}\\ AB=AC& \text{Given}\\ \begin{array}{l}OB=OC\\ \Delta AOB\cong \Delta AOC\\ \angle AOB\cong \angle AOC\end{array}& \begin{array}{l}\text{Given}\\ \text{By SSS}\\ \text{By CPCT}\end{array}\end{array}$

Therefore, the answer is no because data is insufficient.