How to Classify Triangles - Acute, Obtuse, Right

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Mahalo math expert Allison Moffett shows you how to classify triangles.

Intro to Triangles
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A triangle is a two-dimensional object that is composed of three sides.  The point where two sides of a triangle meet is known as a vertex.  An angle is created at the vertex.  A triangle not only has three sides, it also has three vertices.cThe values of all of the interior angles of a triangle add up to 180°. The interior angles of the triangle can be acute, obtuse or right angles. Angles are named by whether they are more than, less than or equal to 90°. The types of interior angles that a triangle has will determine its classification. This differs from the other type of classification that relates to the lengths of the line segments that make up the triangle.c

Step 1: Classifying Acute Triangles
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An acute angle is one that measures less than 90°. Triangles that are composed of all acute angles are named acute triangles.c Use a protractor to measure each angle of the triangle at its vertex.c  If none of the angles measure at least 90°, then the triangle is classified as acute.c 

Step 2: Classifying Obtuse Triangles
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Obtuse angles are ones that measure more than 90° but less than 180°.  If a triangle contains an obtuse angle, it is classified as an obtuse triangle.  An obtuse triangle will only have one obtuse angle. The other two angles will be acute. You can use a protractor to measure all of the angles at their vertices.c  An arc is usually drawn at the vertex of the obtuse angle to show that the triangle is obtuse.c 

Step 3: Classifying Right Triangles
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If a triangle contains one 90° angle, it is classified as a right triangle. A 90° angle is very distinct as it will have one line segment that is perpendicular to another line segment, making an "L" or a backwards "L" shape.  A right triangle will have only one right angle.  Use a protractor to measure the angle to verify that it is 90°.  The other two angles of this triangle will be acute angles.
c  The right angle is distinguished from the other angles by drawing a box in the vertex.c 
A quality that is different about right triangles than other triangles is the proportions of the line segments that make up the triangle.  A concept known as
Pythagorean's Theorem states that the sum of the squares of the two shorter sides is equal to the square of the longest side.  The formula for this is a² + b² = h², where"a" and "b" are the two short segments and "h" is the longest line segment because it is opposite the right angle.  The letter "h" is used because this line segment is named the hypotenuse.c

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