Altitudes and Perpendiculars

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Examples: Perpendiculars and Altitudes

Perpendicular

One line is perpendicular to another line when the angle between them is 90 degrees.

In the image above, the angle between line segment AB and AC is 90 degrees, therefore those two line segments are perpendicular.

We use a little right angle, or square, to indicated perpendicularity:

Altitude

In general, altitude means height.

For triangles, an altitude is a line going through a point that is perpendicular to the opposite side (of that point). Every triangle has 3 altitudes.

The altitudes are not always inside the triangle:

How many altitudes are inside an equilateral triangle?

Choose one answer

Stretch your creativity

Contest problems rarely look like the examples you studied. Solving one means finding your own way in. These are real problems from the AMC 12 and AIME, the national math competitions for middle and high school students, each with a worked solution on LIVE by Po-Shen Loh.

Type a concept, like “slope” or “photosynthesis”.

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