Triangles and Their Angles

Lesson Plan - Get It!

Audio:

In the previous Related Lesson, found in the right-hand sidebar, you learned that triangles can be classified by their sides.

Draw a picture of an equilateral triangle, an isosceles triangle, and a scalene triangle. Remember, triangles are made of three straight lines, so use a straight edge to draw your triangles. Then, show your teacher or parent your drawings and explain what makes each triangle equilateral, isosceles, or scalene.

You can classify a triangle by its sides, and you can also classify it by its angles.

You were able to determine what types of sides different triangles had by measuring the sides with a ruler. How do you think you measure the angles of a triangle so you can classify it by its angles?

To measure the angles of a triangle, you need a protractor. If you are uncertain how to use a protractor, watch the MashUp Math video, How Do I Measure An Angle Using a Protractor? | 4th Grade Math, or read the article Using a Protractor (Math is Fun). If you could use some practice with a protractor, make sure to look at the examples at the bottom of the Math is Fun page.

Knowing how to use a protractor is essential to classifying a triangle by its angles. Like triangles classified by their sides, there are three names given to triangles classified by their angles: acute triangle, obtuse triangle, and right triangle.

The first type of triangle is an acute triangle. Before measuring the angles of the triangle below, tell your teacher or parent what you notice about the triangle's angles. Then, measure each angle to find out if your observations and predictions were correct.

Acute triangles are composed of all acute angles (angles that are less than 90 degrees). You should have noticed that the angles of this triangle are all less than 90 degrees. This triangle has angles that are the same, but this is not always the case with an acute triangle. Sometimes the angles will be different. The important thing to remember is that acute triangles have "all cute" little angles that measure less than 90 degrees.

The next type of triangle you need to know is an obtuse triangle. Based on what you already know about the term "obtuse," what do you think an obtuse triangle is? Use the triangle pictured below to help you develop a definition. Share your definition with your teacher or parent.

You should have said that obtuse triangles have one obtuse angle (an angle that is greater than 90 degrees) and two acute angles. Measure each of the angles of the triangle above. Does it have one obtuse angle?

The last name given to a triangle classified by its angles is a right triangle. Describe the angles on the triangle pictured below your teacher or parent.

This triangle has one right angle (an angle that measures exactly 90 degrees) and two acute angles. Measure each of the angles of the triangle. Show your teacher or parent which angle is a right angle.

Triangles can only ever have one side name and one angle name at a given time. Triangles can never fit the criteria for more than one side name or more than one angle name. Look at the triangle below. Tell your teacher or parent how you would classify it by both its sides and angles.

The triangle pictured above is both scalene and obtuse.

You now know the three ways to name triangles based on their angles. Tell your teacher or parent each of these names and describe each type of triangle. Then, move on to the Got It? section to practice identifying each type of triangle.