Which of the following is the height in triangle ABC?
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Which of the following is the height in triangle ABC?
Let's remember the definition of height of a triangle:
A height is a straight line that descends from the vertex of a triangle and forms a 90-degree angle with the opposite side.
The sides that form a 90-degree angle are sides AB and BC. Therefore, the height is AB.
AB
Is the straight line in the figure the height of the triangle?
Look for the right angle symbol (small square) where a line meets a side! The height is the line segment that forms this 90° angle with the opposite side.
Only in special cases! In a right triangle, the two sides that form the right angle can serve as heights to each other. But usually, heights are separate line segments drawn perpendicular to the sides.
AC and BC are sides of the triangle, not heights. A height must be perpendicular to a side. In this diagram, AB is perpendicular to BC, making AB the height.
Look for visual clues like the line appearing to form a perfect corner with the base. Heights are always drawn at exactly 90 degrees, making them look like they form square corners.
Yes! Every triangle has three heights - one from each vertex to the opposite side. But in any given problem, you're usually asked to identify one specific height.
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