Q3. - Geometry

Question

Describe how you would construct each of the following:

The median of $\Delta ABC$ that contains vertex $B$.

Step-by-Step Solution

Answer

The construction of median of $\Delta ABC$is described. 

Step 1. Given information.

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

Step 2. Concept used.

A line segment joining a vertex to the midpoint of the opposite side.

Step 3. Solution.

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 $X and Y$.

• 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.

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