Types of Triangles

Definition: Triangles have three sides. There are many different ways to classify triangles:

Acute: Three angles less than 90 degrees

Obtuse: One angle greater than 90 degrees

Right: One angle equal to 90 degrees

Equilateral: Three congruent sides (and angles)

Isosceles: Two congruent sides (and angles)

Scalene: No congruent sides (or angles)

239px-Triangles.svg

Example: Classify the following triangles based on the given information. Which type of triangle is not represented?

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Solution:

Triangle 1: This triangle has three unique angles and all three are less than 90 degrees. Based on this information, we can classify Triangle 1 as:
Acute scalene triangle

Triangle 2: This triangle has one angle equal to 90 degree (right angle). Based on these traits, we can classify Triangle 2 as:
Right triangle

Triangle 3: This triangle has two congruent angles, and one angle greater than 90 (obtuse). Based on these traits, we can classify Triangle 3 as:
Obtuse isosceles triangle

Triangle 4: This triangle has three unique angles, one of which is greater than 90 (obtuse). Based on these traits, we can classify Triangle 4 as:
Obtuse scalene triangle

Which type of triangle is not represented?: There is no equilateral triangle represented in the figures.

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