Chapter 10.2, Problem 3CE

To determine

To describe: the construction of median of $\Delta ABC.$

Explanation of Solution

Given information:

The given statement is “The median of $\Delta ABC$ that contains vertex $B$ ”.

The procedure to construct median of$\Delta ABC$:

• Consider the line segment $\overline{AC}$ .
• Choose a radius greater than $\frac{1}{2}\overline{AC}$ .
• Using the above radius and A as centre draw two arcs above and below the line $\overline{AC}$ .
• Using the same radius and C as centre draw two arcs above and below the line $\overline{AC}$ .
• Label the intersecting the points as $X\&Y$ .
• Observe $\overline{XY}$ is the perpendicular bisector of $\overline{AC}$ .
• The intersection point of $\overline{XY}\&\overline{BC}$ is the midpoint of $\overline{AC}$ label the point as M

Draw the median $\overline{BM}$

The construction is shown below.

  

Hence, the construction of median of $\Delta ABC$ is described.