# Altitudes in right, acute, obtuse and equilateral triangles.

Definitions:

**An altitude** of a triangle is a line segment through the vertex and perpendicular to the base.

All three altitudes intersect at the same point called **orthocenter**.

**Right Triangle** - has a 90 degree angle, altitudes meet at the vertex of the right angle

**Acute Triangle** - has an angle less than 90 degrees, altitudes meet inside the triangle

**Obtuse Triangle** - has an angle more than 90 degrees and has an orthocenter outside of the triangle.

**Equilateral Triangle** - is a triangle where all of the sides are equal to one another. An equilateral triangle also has equal angles, 60 degrees each. In an equilateral triangle the orthocenter lies inside the triangle and on the perpendicular bisector of each side of the triangle.

Let's look at a question from the geometry regent:

If the altitudes of a triangle meet at one of the triangle’s vertices, then the triangle is

(1) a right triangle (2) an acute triangle

(3) an obtuse triangle (4) an equilateral triangle

Answer: **Choice 1 (right triangle)** is the correct answer choice

Explanation: From the definitions above, we see that the altitudes of a right triangle intersect and form an orthocenter at its vertex.

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