A height is a line segment that connects a vertex to its opposite side and is perpendicular to the opposite side.
A triangle’s height can be drawn two ways:
Sometimes a triangle’s height is located outside of the triangle itself.
We can use a compass and ruler to sketch a triangle’s height by following these steps:
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Open the compass so that its opening is equal to the distance between the triangle’s vertex where the height will come from and another vertex of the triangle. Keep the same open setting for every stage of the construction.
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Place the compass’ sharp point on the top of the triangle where the height will come from and draw an arc that intersects the triangle’s base. This gives a new point.
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Place the compass’ sharp point on the end of the triangle’s base used in step 1 and draw a circle passing through the point found in step 2.
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Place the compass’ sharp point on the point found in step 2 and draw a circle of the same size.
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Using a ruler, connect the intersections of the two circles. The part of the straight line inside the triangle corresponds to its height.
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The technique could also be performed from the other side of the triangle. The point found in step 2 would be on the extension of the triangle’s base.
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We can use a ruler to draw the triangle’s height by following these steps:
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Place one side of the set square’s right angle on the triangle’s base.
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Line up the other side of the set square’s right angle with the top of the triangle.
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Draw the segment that starts from the vertex and intersects perpendicular to the triangle’s base. This segment is the triangle’s height.
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