Chapter 10.5, Problem 3ST2

To determine

Draw a segment about half as long as the width of your paper.Then divide the segment by construction into two segments whose lengths have the ratio 2:1.

Explanation of Solution

Given:

  $\overline{AB}$ is 15 cm long.

Calculation:

Draw $\overline{AB}$ half as long as the paper.

  

To divide $\overline{AB}$ into 3 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, and T so that AR=RS=ST.
3. Draw $\overline{TB}$ .
4. At R, and S construct lines parallel to $\overline{TB}$ , intersecting $\overline{AB}$ in X, and Y.

$\overline{AX},\overline{XY},\overline{YB}$ are congruent parts of $\overline{AB}$ .

  

We have divided $\overline{AB}$ into 3 equal segments.

So, they have ratio 1:1:1.

We need two segments with ratio 2:1.

So, we will join first two parts to get the ratio of two resulting segments as 2:1 .

  

  $\overline{AY}:\overline{YB}=2:1$