Chapter 6.1, Problem 19CE

(a)

To determine

To Complete: the statement $AB\underset{\_}{?}AC$ by $<,=,\text{ or >}$ for the figure shown.

Answer to Problem 19CE

  $=$

Explanation of Solution

Given:

Figure is shown below.

  

Calculation:

Since, in a triangle having two equal angles, sides opposite to these angles are also equal.

  $m\angle B=m\angle C=70$

Therefore, $AB=AC$

Therefore, the answer is $=$ .

(b)

To Complete: the statement $AB\underset{\_}{?}AX+XB$ by $<,=,\text{ or >}$ for the figure shown.

To determine

  $=$

Answer to Problem 19CE

  $=$

Explanation of Solution

Given:

Figure is shown below.

  

Calculation:

Since, AX and XB coincides on AB therefore.

  $AB=AX+XB$

Therefore, the answer is $=$ .

(c)

To Complete: the statement $AB\underset{\_}{?}XB$ by $<,=,\text{ or >}$ for the figure shown.

To determine

  $>$

Answer to Problem 19CE

  $>$

Explanation of Solution

Given:

Figure is shown below.

  

Calculation:

Since, AX and XB coincides on AB therefore.

  $AB=XB+AX$

If $a=b+c\text{and }c>0,\text{then}a>b$

  $AB>XB$

Therefore, the answer is $>$ .

(d)

To Complete: the statement $AC\underset{\_}{?}XB$ by $<,=,\text{ or >}$ for the figure shown.

To determine

  $>$

Answer to Problem 19CE

  $>$

Explanation of Solution

Given:

Figure is shown below.

  

Calculation:

Since, in a triangle having two equal angles, sides opposite to these angles are also equal.

  $m\angle B=m\angle C=70$

Therefore, $AB=AC$

Since, AX and XB coincides on AB therefore.

  $\begin{array}{l}AB=XB+AX\\ \Rightarrow AC=XB+AX\end{array}$

If $a=b+c\text{and }c>0,\text{then}a>b$

  $AC>XB$

Therefore, the answer is $>$ .