Q5. - Geometry

Question

Describe how you would construct each of the following:

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

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$A$”.

Step 2. Concept used.

An altitude of a triangle is a line segment through a vertex and perpendicular to (i.e., forming a right angle with) a line containing the base (the side opposite the vertex).

Step 3. Solution.

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

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

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

Points $X \&Y$.

• With $X \&Y$as centers and suitable radius draw two arcs that intersect at point $Z$.

• Draw the line$\overline{AZ}$.

• The  altitude is$\overline{AM}$

The construction is shown below: 

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