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Course: 4th grade   >   Unit 11

• Classifying triangles

Classifying triangles by angles

• Worked example: Classifying triangles
• Classify triangles by angles
• Classify triangles by side lengths
• Classify triangles by both sides and angles
• Types of triangles review

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Video transcript

Triangle Classification by Sides

Classifying triangles by sides.

A triangle can be classified based on its characteristics. One way to classify triangles is by their sides or by comparing the lengths of the triangle’s three sides . Based on how many congruent sides a triangle has, it can either be classified as an Equilateral, Isosceles or Scalene triangle.

HINT : The tick marks indicate congruent sides. For example, if both sides of a triangle have the same number of tick marks, it means that both sides have the same measure.

Let’s now look at each type of triangle classified by its sides closely.

EQUILATERAL TRIANGLE – All three sides of the triangle are congruent or have an equal measure. In other words, the triangle has 3 congruent sides .

ISOSCELES TRIANGLE – At least two sides of the triangle are congruent or have an equal measure. Simply put, the triangle has 2 congruent sides

SCALENE TRIANGLE – All sides of the triangle have different measures. Thus, no sides are congruent or the triangle has 0 congruent sides

Example Problems on How to Classify Triangles by their Sides

Example 1 : Classify each triangle by its sides.

a. The tick marks on this triangle indicate that each side has a different measure. Therefore, none of the sides are congruent which makes this a scalene triangle .

b. All three sides of this triangle are congruent so this is an equilateral triangle .

Example 2 : Classify the triangles given the lengths of their sides.

• Triangle M – Sides: 8 cm, 8 cm, 3 cm
• Triangle K – Sides: 2 in., 2 in., 2 in.
• Triangle P – Sides: 4 ft, 7 ft, 7 ft
• Triangle V – Sides: 5 mm, 10 mm, 6 mm

Triangle M: Since at least two sides have the same equal measure, this triangle is an isosceles triangle .

Triangle K: This is an equilateral triangle because all sides are congruent.

Triangle P: Two out of the three sides of this triangle measure 7 ft. Thus, it is an isosceles triangle .

Triangle V: It is obvious that this is a scalene triangle . It has 0 congruent sides because the triangle has different side lengths.

Example 3 : What is the measure of [latex]\overline {AC} [/latex]?

At first look, we can immediately tell that this is an isosceles triangle. Why? Because the tick marks tell us that there are two congruent sides, i.e. [latex]\overline {AC}[/latex] and [latex]\overline {CB} [/latex].

TIP : Do not assume immediately that the side lengths of the triangle are congruent based on appearance. They must be marked as congruent (look for the tick marks) or if the measurements are not already given, measure them to check the length of each side.

So far we are given two measurements:

• [latex]\overline {AB}[/latex] = 7 cm
• [latex]\overline {CB} [/latex] = 4.5 cm

Our task now is to determine the length of [latex]\overline {AC} [/latex]. However, since we know that [latex]\overline {CB} [/latex] and [latex]\overline {AC} [/latex] are congruent ([latex]\overline {CB} \cong \overline {AC} [/latex]), this means that their measures are the same.

Therefore, the length of [latex]\overline {AC} [/latex] is 4.5 cm .

You may also be interested in these related math lessons or tutorials:

Classifying Triangles by Angles

Area of a Triangle

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4.3: Classify Triangles by Side Measurement

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Classify triangles as scalene, isosoles or equalateral by identifying the number of equal sides.

Triangle Classification by Side Lengths

Tasha goes sailing with her father on her father's old boat. The sail looks like a triangle . All of the sides of the sail are different lengths. Tasha wants to classify the triangle but she isn't sure how to name it. Given the side lengths of the triangle, how can Tasha classify the triangle?

In this concept, you will learn how to classify triangles by their side lengths.

Classifying Triangles by Side Lengths

You can use the lengths of the sides to help you classify triangles.

Let’s look at how to classify triangles according to side length.

An equilateral triangle has side lengths that are the same. Here is an example.

These little lines let you know that the side lengths are the same. Sometimes you will see these and sometimes you won’t. You may have to figure it out on your own or by measuring with a ruler.

A scalene triangle is a triangle where the lengths of all three sides are different. Here is an example of a scalene triangle.

You can see that all three sides of the triangle are different lengths.

An isosceles triangle has two side lengths that are the same and one side length that is different. Here is an example of an isosceles triangle.

Example \(\PageIndex{1}\)

Earlier, you were given a problem about Tasha and her sail.

Her sail is shaped like a triangle with different side lengths. What classification should Tasha give the triangle?

First, determine if any of the side lengths are the same.

Then, classify the triangle.

The answer is a scalene triangle.

Example \(\PageIndex{2}\)

Classify this triangle as scalene, isosceles or equilateral according to its side lengths.

Side lengths, 6 cm, 4 cm, 6 cm

Angles 70, 70, 40 degrees

Next, determine how many side lengths are the same.

The answer is an isosceles triangle.

Example \(\PageIndex{3}\)

Classify this triangle according to its side lengths.

Example \(\PageIndex{4}\)

Classify the triangle according to its side lengths.

All of the side lengths are the same

Equilateral

The answer is an equilateral triangle.

Example \(\PageIndex{5}\)

Answer the following questions using what you have learned about triangles their angles and side lengths.

• If a triangle is a right triangle, then how many angles are acute?
• How many angles in a right triangle are right angles?
• How many degrees are there in a right triangle?
• What is an obtuse angle?
• How many obtuse angles are in an obtuse triangle?
• If there is one obtuse angle, how many angles are acute?
• If a triangle is equiangular, what is the measure of all three angles?
• What does the word “interior angle” mean?
• True or false. The side lengths of a scalene triangle are all equal.
• True or false. The side lengths of a scalene triangle are all different.
• True or false. The side lengths of an equilateral triangle are all equal.
• True or false. An isosceles triangle has two side lengths the same and one different.
• True or false. A scalene triangle can also be an isosceles triangle.
• True or false. An equilateral triangle is also equiangular.
• True or false. A scalene triangle can not be an acute triangle.

Review (Answers)

To see the Review answers, open this PDF file and look for section 9.8.

Additional Resources

Interactive Element

Video: Angle Relationships and Types of Triangles

Practice: Classify Triangles by Side Measurement

Classifying triangles by their sides and angles

We classify a bunch of triangles as either acute, right, or obtuse (classification by angles), and as either scalene, isosceles, or equilateral (classification by sides).

Then we tackle two drawing problems that concern triangles. Drawing is at the heart of what geometry is all about and it is both a hands-on activity, which students like, and also requires geometric reasoning about the attributes.

This lesson is meant for 5th grade and onward.

Classify quadrilaterals — video lesson

Math Mammoth Geometry 1 — a self-teaching worktext with explanations & exercises (grades 4-5)

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McGraw Hill My Math Grade 3 Chapter 14 Lesson 3 Answer Key Triangles

All the solutions provided in  McGraw Hill My Math Grade 3 Answer Key PDF Chapter 14 Lesson 3 Triangles will give you a clear idea of the concepts.

McGraw-Hill My Math Grade 3 Answer Key Chapter 14 Lesson 3 Triangles

Talk About It

Identify each triangle with what you discovered about the side lengths.

Question 1. No side lengths are the same. Triangle(s) _____________ Answer: In triangle D no side lengths are the same.

Question 2. All 3 side lengths are the same. Triangle(s) _____________ Answer: In triangle A and triangle B all 3 side lengths are the same.

Question 3. Exactly 2 side lengths are the same. Triangle(s) _____________ Answer: In triangle C exactly 2 side lengths are the same.

Mathematical PRACTICE Draw a Conclusion Refer to the activity above for Exercises 4-5.

Question 4. Which triangle has an angle greater than a right angle? Answer: The triangle B has an angle greater than a right angle.

Question 5. Which triangle has all 3 angles that are less than a right angle? Answer: The triangle C has all 3 angles that are less than a right angle.

Question 6. Explain how a triangle is a special kind of polygon. Answer: The triangle is special kind of polygon. It has only 3 sides. for the polygon one or two sides are possible. Triangle is least number of possible sides. So, it is polygon.

Practice It

Measure the sides of each triangle below to the nearest quarter of an inch. Then state the number of sides with equal lengths.

Compare the angles of each triangle. Then circle the correct description.

Question 15. Circle the triangles on this page that are right triangles. Answer: There are 2 right triangles on this page they are

Write About It

Question 19. How are all triangles the same and how can they be different? Answer: All triangles are similar when the corresponding angles are congruent. The similar triangles have same shape but they have different size.

McGraw Hill My Math Grade 3 Chapter 14 Lesson 3 My Homework Answer Key

Problem Solving

Question 6. Refer to Exercise 5. How many angles are less than a right angle? Answer: The all the 3 angles are less than than a right angle.

Vocabulary Check

Fill in the missing word.

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Explanation:

Find the value of x.

Model with Mathematics Refer to the graphic novel below. Classify the triangle formed by the cabin, ropes course, and mess hall by its angles and sides.

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Chapter 4, Lesson 1: Classifying Triangles

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