Given the following triangle:
Write down the height of the triangle ABC.
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Given the following triangle:
Write down the height of the triangle ABC.
To determine the height of triangle , we need to identify the line segment that extends from a vertex and meets the opposite side at a right angle.
Given the diagram of the triangle, we consider the base and need to find the line segment from vertex to this base.
From the diagram, segment is drawn from and intersects the line (or its extension) perpendicularly. Therefore, it represents the height of the triangle .
Thus, the height of is segment .
BD
True or false:
DE not a side in any of the triangles.
BD is the height because it's perpendicular to the base AC. Look for the small square symbol in the diagram - this shows the 90-degree angle that makes BD a true height!
Yes! Every triangle has three heights - one from each vertex to the opposite side. In this problem, BD is the height from vertex B to base AC.
Not always! In obtuse triangles, some heights fall outside the triangle on the extended base line. The height is still measured as the perpendicular distance.
Look for these clues:
AD goes from vertex A, but we need the height to the base AC. Since A is already on the base AC, AD cannot be perpendicular to AC - it would just be part of the base!
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