Question

Draw three noncollinear points $R,S,$and $T.$ Construct a triangle whose sides have $R,S,$and $T$ as midpoints.

Short answer

The figure is,

Step-by-step solution

Step 1. Given information.

Three noncollinear points$R,S,$and $T$are given.

Step 2. Follow the ways.

Consider the following ways-

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 $\overline{AC}$.

Step 3. Construct the figure.

Therefore, the required figure drawn above.