Triangle Classification by
Angles
Jen Kershaw
Kimberly Hopkins
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Printed: May 11, 2016
AUTHORS
Jen Kershaw
Kimberly Hopkins
www.ck12.org
C HAPTER
Chapter 1. Triangle Classification by Angles
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Triangle Classification by
Angles
In this concept, you will learn how to use angles to classify triangles.
Let’s Think About It
Michael’s mother bought a caddy that fits in a corner. She uses the caddy to store their brooms and mops in the
garage. His mother’s caddy had the appearance of a right triangle when viewed from above and fit perfectly in the
corner. Michael liked the caddy, but he couldn’t afford to buy one like hers, so he decided to make his own. He
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bought wood and nails and put it together, but when he tried to put it in the corner in his room, it wouldn’t fit. He
measures the angles of his caddy and realizes that the top is the triangle below:
What is the classification of Michael’s triangle?
In this concept, you will learn how to use angles to classify triangles.
Guidance
The prefix “tri” means three. Triangle means three angles.
To classify a triangle according to its angles, you must look at the angles inside the triangle. Use the number of
degrees in these angles to classify the triangle. Let’s look at a picture of a triangle to explain.
Look at the measure of each angle inside the triangle to figure out what kind of triangle it is. There are four types of
triangles based on angle measures.
A right triangle is a triangle that has one right angle and two acute angles. One of the angles in the triangle measures
90◦ and the other two angles are less than 90. Here is a picture of a right triangle.
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Chapter 1. Triangle Classification by Angles
You can see that the 90 degree angle is the one in the bottom left corner. You can even draw in the small box to
identify it as a 90 degree angle. If you look at the other two angles you cans see that those angles are less than 90
degrees and are acute.
Let’s look at an example of a right angle.
This triangle has one 90◦ angle and two 45◦ angles. Find the sum of the three angles.
90 + 45 + 45 = 180◦
The sum of the three angles of a triangle is always equal to 180◦ .
In an equiangular triangle, all three of the angles are equal.
The three angles of this triangle are equal. This is an equiangular triangle.
You know that the sum of the three angles is equal to 180o , therefore, for all three angles to be equal, each angle
must be equal to 60◦ .
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60 + 60 + 60 = 180◦
The sum of the angles is equal to 180◦ .
In an acute triangle, all three angles of the triangle are less than 90 degrees. Here is an example of an acute triangle.
All three of these angles measure less than 90 degrees.
33 + 80 + 67 = 180◦
The sum of the angles is equal to 180◦ .
An obtuse triangle has one angle that is greater than 90 and two angles that are less than 90.
130 + 25 + 25 = 180◦
The sum of the angles is equal to 180◦ .
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Chapter 1. Triangle Classification by Angles
Guided Practice
Identify the type of triangle according to its angles.
First, list the angle measures.
10, 75, 95
Next, determine if any of the angles are equal to 90 degrees or larger than 90 degrees.
Yes, one angle is larger than 90 degrees
Then, classify the triangle.
Obtuse
The answer is an obtuse triangle.
Examples
Example 1
Identify the type of triangle according to its angles.
First, list the angle measures.
30, 70 and 80
Next, determine if any of the angles are equal to 90 degrees or larger than 90 degrees.
No
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Then, classify the angle.
Acute
The answer is an acute triangle.
Example 2
Identify the type of triangle according to its angles.
First, list the angle measures.
35, 55 and 90
Next, determine if any of the angles are equal to 90 degrees or larger than 90 degrees.
Yes, one of the angles is equal to 90 degrees
Then, classify the angle.
Right
The answer is a right triangle
Example 3
Classify the triangle by looking at the sum of its angles.
40o + 60o + 80o = 180o
First, list the angle measures.
40, 60 and 80
Next, determine if any of the angles are equal to 90 degrees or larger than 90 degrees.
No
Then, classify the angle.
Acute
The answer is an acute triangle.
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Chapter 1. Triangle Classification by Angles
Follow Up
Remember Michael and his caddy? He tried to build a caddy like his mother’s caddy. Her caddy looked like a right
triangle from above but he ended up building one that had the following measures and appearance from above:
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What is the classification of Michael’s triangle?
First, list the angle measures.
20, 20, 140
Next, determine if any of the angles are equal to 90 degrees or larger than 90 degrees.
Yes, one angle is larger than 90 degrees
Then, classify the triangle.
Obtuse
The answer is an obtuse triangle. Michael created an obtuse triangle instead of a right triangle.
Video Review
MEDIA
Click image to the left or use the URL below.
URL: https://www.ck12.org/flx/render/embeddedobject/168012
Explore More
Classify each triangle according to its angles.
1.
2.
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Chapter 1. Triangle Classification by Angles
3.
4.
5.
Classify the following triangle by looking at the sum of the angle measures.
6.
40 + 55 + 45 = 180◦
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7.
20 + 135 + 25 = 180◦
8.
30 + 90 + 60 = 180◦
9.
60 + 60 + 60 = 180◦
10.
110 + 15 + 55 = 180◦
11.
105 + 65 + 10 = 180◦
12.
80 + 55 + 45 = 180◦
13.
70 + 45 + 65 = 180◦
14.
145 + 20 + 15 = 180◦
15.
60 + 80 + 40 = 180◦
Answers for Explore More Problems
To view the Explore More answers, open this PDF file and look for section 9.7.
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