Chapter 10.5, Problem 3WE

(a)

To determine

Use Construction 12 to divide $\overline{AB}$ into five congruent segments.

Explanation of Solution

Given:

  $\overline{AB}$ is 15 cm long.

Calculation:

Draw $\overline{AB}$ 15 cm long.

  

To divide $\overline{AB}$ into 5 congruent segments :

1. Choose any point Z not on $\overline{AB}$ . Draw $\overrightarrow{AZ}$ .
2. Use any radius , start with A as center and mark off R , S, T , U , and V so that AR=RS=ST=TU=UV.
3. Draw $\overline{VB}$ .
4. At R, S, T, and U construct lines parallel to $\overline{VB}$ , intersecting $\overline{AB}$ in W, X , Y , and Z.

$\overline{AW},\overline{WX},\overline{XY},\overline{YZ},\overline{ZB}$ are congruent parts of $\overline{AB}$ .

  

(b)

To determine

Can construction 4 be used to divide $\overline{AB}$ into five congruent segments.

Answer to Problem 3WE

No

Explanation of Solution

Given:

  $\overline{AB}$ is 15 cm long.

Calculation:

Since Construction 4 is used to draw a perpendicular bisector to a line.

So, it can be used only to divide a given line into even number of segments.

Since here, we need to divide the line segment into 5 congruent segments, which is odd, so, Construction 4 cannot be used to do so.

(c)

To determine

Divide $\overline{AB}$ into two segments that have ratio 2:3

Explanation of Solution

Given:

  $\overline{AB}$ is 15 cm long.

Calculation:

From part (a) , we have divided $\overline{AB}$ into 5 equal segments.

So, they have ratio 1:1:1:1:1.

We need two segments with ratio 2:3.

So, we will join first two parts and last three equal parts to get 2:3 ratio.