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Triangle Classification
Bill Zahner
Lori Jordan
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Printed: May 10, 2016
AUTHORS
Bill Zahner
Lori Jordan
www.ck12.org
C HAPTER
Chapter 1. Triangle Classification
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Triangle Classification
Here you’ll learn how to classify a triangle based on its angles and sides.
What if you were given the angle measures or side lengths of several triangles and were asked to group them based
on their properties? After completing this Concept, you’ll be able to classify a triangle as right, obtuse, acute,
equiangular, scalene, isosceles, and/or equilateral.
Watch This
MEDIA
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URL: https://www.ck12.org/flx/render/embeddedobject/136973
CK-12 Foundation: Chapter1TriangleClassificationA
Watch this video starting at around 2:30.
MEDIA
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James Sousa: Types of Triangles
Guidance
A triangle is any closed figure made by three line segments intersecting at their endpoints. Every triangle has three
vertices (the points where the segments meet), three sides (the segments), and three interior angles (formed at each
vertex). All of the following shapes are triangles.
You might have also learned that the sum of the interior angles in a triangle is 180◦ . Later we will prove this, but for
now you can use this fact to find missing angles. Angles can be classified by their size: acute, obtuse or right. In
any triangle, two of the angles will always be acute. The third angle can be acute, obtuse, or right. We classify each
triangle by this angle.
Right Triangle: When a triangle has one right angle.
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Obtuse Triangle: When a triangle has one obtuse angle.
Acute Triangle: When all three angles in the triangle are acute.
Equiangular Triangle: When all the angles in a triangle are congruent.
We can also classify triangles by its sides.
Scalene Triangle: When all sides of a triangle are all different lengths.
Isosceles Triangle: When at least two sides of a triangle are congruent.
Equilateral Triangle: When all sides of a triangle are congruent.
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Chapter 1. Triangle Classification
Note that by the above definitions, an equilateral triangle is also an isosceles triangle.
Example A
Which of the figures below are not triangles?
B is not a triangle because it hasone curved side. D is not a closed shape, so it is not a triangle either.
Example B
Which term best describes 4RST below?
This triangle has one labeled obtuse angle of 92◦ . Triangles can only have one obtuse angle, so it is an obtuse
triangle.
Example C
Classify the triangle by its sides and angles.
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We are told there are two congruent sides, so it is an isosceles triangle. By its angles, they all look acute, so it is an
acute triangle. Typically, we say this is an acute isosceles triangle.
Watch this video for help with the Examples above.
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CK-12 Foundation: Chapter1TriangleClassificationB
Guided Practice
1. How many triangles are in the diagram below?
2. Classify the triangle by its sides and angles.
3. Classify the triangle by its sides and angles.
Answers:
1. Start by counting the smallest triangles, 16. Now count the triangles that are formed by four of the smaller
triangles.
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Chapter 1. Triangle Classification
There are a total of seven triangles of this size, including the inverted one in the center of the diagram.Next, count
the triangles that are formed by nine of the smaller triangles. There are three of this size. And finally, there is one
triangle formed by the 16 smaller triangles. Adding these numbers together, we get 16 + 7 + 3 + 1 = 27.
2. This triangle has a right angle and no sides are marked congruent. So, it is a right scalene triangle.
3. This triangle has an angle bigger than 90◦ and two sides that are marked congruent. So, it is an obtuse isosceles
triangle.
Interactive Practice
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Explore More
For questions 1-5, classify each triangle by its sides and by its angles.
1.
2.
3.
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4.
5.
6. Can you draw a triangle with a right angle and an obtuse angle? Why or why not?
7. In an isosceles triangle, can the angles opposite the congruent sides be obtuse?
8. Construction Construct an equilateral triangle with sides of 3 cm. Start by drawing a horizontal segment of 3
cm and measure this side with your compass from both endpoints.
9. What must be true about the angles of your equilateral triangle from #8?
For 10-14, determine if the statement is ALWAYS true, SOMETIMES true, or NEVER true.
10.
11.
12.
13.
14.
Obtuse triangles are isosceles.
A right triangle is acute.
An equilateral triangle is equiangular.
An isosceles triangle is equilaterals.
Equiangular triangles are scalene.
In geometry it is important to know the difference between a sketch, a drawing and a construction. A sketch is
usually drawn free-hand and marked with the appropriate congruence markings or labeled with measurement. It
may or may not be drawn to scale. A drawing is made using a ruler, protractor or compass and should be made to
scale. A construction is made using only a compass and ruler and should be made to scale.
For 15-16, construct the indicated figures.
15. Construct a right triangle with side lengths 3 cm, 4 cm and 5 cm.
16. Construct a 60◦ angle. ( Hint: Think about an equilateral triangle.)
Answers for Explore More Problems
To view the Explore More answers, open this PDF file and look for section 1.11.
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