Grade 6 | Lesson 18

Mathematics

Lesson Overview

6th Grade Mathematics

***You will need a protractor and ruler to complete this lesson. If you need help with where to obtain these, please contact Mrs. Warren (dean@theschools.com) or your online academic advisor (if applicable).***

• Classification of Triangles

6th Grade Mathematics

We started to examine triangles, via constuctions, in the previous lesson, and in this one we'll take a look at the various types!

Classification of Triangles
All triangles have 3 sides and 3 angles. Let's look at how we can classify triangles by looking at their sides.

There are three types of triangles that are classified by the length of their sides: equilateral, isosceles and scalene.

Equilateral ("Equi"= equal, "Lateral"= sides)
This type of triangle has sides which are all equal. Slash marks on sides indicate they are equal.

Isosceles ("Iso"= same, "sceles"= legs)
This type of triangle has at least 2 sides which are equal, which are called the base angles. The remaining angle is called the top angle. For any isosceles triangle, the angles, adjacent to the side that is of different length, are equal to each other.

Scalene
This type of triangle has at no sides which are equal.

There are three types of triangles that are classified by the measure of their angles: right, obtuse, acute and equiangular.

Right
This type of triangle has a right triangle in its interior. A right angle has a measure of 90°.

Obtuse
This type of triangle has an obtuse angle triangle in its interior. An obtuse angle has a measure greater than 90°.

Acute
This type of triangle has all acute angles in its interior. An acute angle has a measure less than 90°.

Equiangular
This type of triangle has all angles which are equal.

Research It!
Why can't a triangle have more than one obtuse angle?

Here are a few problems to help cement the classification of triangles for you to work on independently.

1) Draw an isosceles triangle (a triangle that has two equal sides). Start out by drawing the two sides that have equal measure and draw the third side last. Use a ruler to make sure they are equal.

2) How do you think the angles of an equilateral triangle relate? What is the measure of the angles of an equilateral triangle? Does the length of the sides matter?

3) Draw an isosceles triangle whose base angles are 40°. What is the top angle? The sides can be any length.

4) Draw an isosceles triangle whose base angles are 75°. What is the top angle? The sides can be any length.

Answers (Only for at-home teacher):
1) Answers will vary
2) They are congruent. 60°. The side length does not matter.
3) 100°
4) 29°