Chapter 10.2, Problem 27WE

To determine

To draw: three noncolinear points $R,S$ and $T$ and to construction a triangle whose sides have $R,S$ and $T$ as midpoints.

Explanation of Solution

Draw a line joining $R$ and $T$ , since $R$ and $T$ are the mid points of two sides, $\overline{RT}$ is parallel to the third side for which $S$ is the midpoint.

Construct a line parallel to $\overline{RT}$ on point $S$ , by constructing $\angle 1=\angle TRS$ .

Since $\overline{RT}$ is half of the third side, open the compass and measures the line $\overline{RT}$ .

Put the compass needle on $S$ and cut both sides at points $B$ and $C$ .

Join the points $B$ and $C$ .

Join the points $B$ and $R$ , and extend the line such that $R$ is the midpoint of $\overline{AB}$ .

Similarly join the points $C$ and $T$ , and extend the line such that $T$ is the midpoint of $\overline{AC}$ .

As shown in the figure below: