Chapter 4.5, Problem 9WE

(a)

To determine

To Find: whether it is possible to prove $\angle AOB\cong \angle AOC$ shown in figure such that $AB=AC$ and $OB=OC$ .

Answer to Problem 9WE

Yes, it is possible.

Explanation of Solution

Given information:

Given figure is.

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

Calculation:

Yes, it possible to prove because two equal sides are given and third one is common in the triangles.

Its proof is shown below.

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 9WE

No.

Explanation of Solution

Given information:

Given figure is.

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

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.