Q4. - Geometry

Question

Describe how you would construct each of the following:

The altitude of $\Delta ABC$ that contain vertex$B$.

Step-by-Step Solution

Answer

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

Step 1. Given information.

The given statement is “The altitude 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 altitude of $\Delta ABC$:

• Consider the line segment$\overline{AC}$ and extend it.

• Using $B$ as centre draw two arcs of same radii that intersects the line$\overline{AC}$ at two 

points$X \&Y$.

• As $X$ and $Y$ as centers with suitable radius draw two arcs that intersect at point $Z$.

• Draw the line $\overline{BZ}$.

• The altitude is $\overline{BM}$.

The construction is shown below:

Therefore, The construction of altitude of $\Delta ABC$ is described.