Question

an altitude of a triangle is a line segment with one endpoint at a vertex of the triangle that is perpendicular to the opposite side of the triangle. construct the altitude in $\triangle abc$ from vertex a. make sure to place a point at the endpoints of the altitude you construct.

Explanation:

Step1: Identify target side

The side opposite vertex A is BC.

Step2: Set compass at vertex A

Open compass to a length greater than the perpendicular distance from A to BC.

Step3: Draw arcs across line BC

Draw two arcs that intersect line BC (or its extension) at two distinct points, say D and E.

Step4: Set compass at point D

Open compass to a length greater than $\frac{1}{2}DE$.

Step5: Draw arc below/above BC

Draw an arc on the side of BC where vertex A is not located.

Step6: Repeat step5 at point E

Draw an arc intersecting the arc from step5 at point F.

Step7: Draw segment AF

Draw a line segment connecting A to the intersection point of AF and BC (call this point G). AG is the altitude, with G on BC.

Step8: Mark endpoints

Place a point at A and a point at G (the intersection of AG and BC).

Answer:

The altitude from vertex A to side BC is constructed as a perpendicular segment $\overline{AG}$, where G lies on line BC, with endpoints marked at A and G.