Construct an Altitude of a Triangle

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High School Math based on the topics required for the Regents Exam conducted by NYSED.
How to construct the altitudes of acute, obtuse and right triangles?

The following diagrams shows how to construct altitudes for an acute triangle and an obtuse triangle. Scroll down the page for more examples and solutions.
Construct Triangle Altitudes

Constructing Triangle Altitudes
Altitudes are defined as perpendicular line segments from the vertex to the line containing the opposite side. In each triangle, there are three triangle altitudes, one from each vertex. In an acute triangle, all altitudes lie within the triangle. In a right triangle, the altitude for two of the vertices are the sides of the triangle. In an obtuse triangle, the altitude from the largest angle is outside of the triangle.

Constructing an altitude inside of the triangle
Using a compass and a straight edge to create the altitude of a triangle that lies inside the triangle

Constructing an altitude outside the triangle
Using a straight edge and a compass to construct an altitude outside of the triangle

Constructing an altitude of a triangle

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