Chapter 10.3, Problem 3ST1

To determine

To draw: a large acute $\Delta ABC$ and to construct altitude $\overrightarrow{AD}$ from vertex $A$ .

Explanation of Solution

Draw a acute triangle $\Delta ABC$ .

Extend the line segment $BC$ .

Use $A$ as center draws two arcs of equal redii that intersects $\overline{BC}$ at point $X$ and $Y$ .

Use $X$ and $Y$ as centers and a suitable radius, draw two arcs that intersect at a point $Z$ .

Draw $\overline{AZ}$ .

Note the point of intersection of $\overline{AZ}$ and $\overline{BC}$ . Label this point as $D$ .

Thus, $\overrightarrow{AD}$ is an altitude of $\Delta ABC$ that contains vertex $A$ .

Draw the figure as below: