Geometry Lesson Plan: Supplementary and Complementary Angles

written by: Keren Perles • edited by: Sarah Malburg • updated: 3/2/2012

Students need hands-on activities in order to truly understand the various concepts in geometry class. You can use this supplementary angles and complementary angles lesson plan to help your students understand the difference between these two types of angles.

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Discovery Learning: An Introductory Activity

Instructing students to memorize the concept of complementary angles and supplementary angles is essentially worthless if they don't understand what the definitions mean. Therefore, a good supplementary and complementary angles lesson plan will focus on making sure that students work with the definitions as much as possible and actively take part in actions that will help them to remember how these two types of angles work.

The first step of a good lesson plan on the subject, therefore, will allow students to discover complementary and supplementary angles on their own. To do this, divide students into groups so that they can interact and help each other work with the problem that you will give. Then draw a horizontal line on the board and encourage students to draw a second line that starts at the first and angles upwards. You can draw several lines - some closer to right angles, and some angled off to the side - to show them their different options. Then instruct them to use a protractor to measure the two angles that are formed on either side of the added line, and to add together the measurements of the two angles. Groups should then share their results with the rest of the class.

Students will probably be surprised to find out that no matter where the additional line was drawn or what the resulting angles were, the final sum is always 180 degrees. As a class, discuss why this might be so. (You may want to represent a straight line as a 90 degree angle stretched an additional ninety degrees, or as an 179 degree angle stretched another 1 degree.)

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Direct Instruction

Write the definitions of supplementary angles and complementary angles on the board, noting that complementary angles add up to 90 degrees and supplementary angles add up to 180 degrees. Have students brainstorm ideas individually to help them remember the difference between the two definitions. Share their hints with the class, perhaps writing a list on the board, and then let each student choose the one that works best for him or her. Examples of these hints might focus on the letter "c" being half of the letter "s," or on the words "compliment" and "supplement."

This is also a good time to point out the spelling of these two commonly misspelled words. Students will probably be familiar with the word "compliment" spelled with an "i," but will need to realize that "complementary" is spelled with an "e" when it refers to angles.

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Review Activity and Assessment

At this point, students can play a short game to help them remember the names and concepts of complementary and supplementary angles. In small groups, students should take turns rolling a set of three dice. On their first turns, they should take the sum on the dice and draw an angle (using their protractors) with the same number of degrees. On each subsequent turn, they should add the sum on the dice to the angle they already have and draw the corresponding angle accordingly. The goal is to get the closest to either the ninety degree mark or the 180-degree mark, without going over. Students can choose to stop rolling the dice whenever they would like.

At the end of this geometry game, students should discuss the results with the class, using the terms "complementary" and "supplementary" angles. Their ability to play this game successfully and discuss the results using the new terms will determine whether this supplementary angles and complementary angles lesson plan has been effective in teaching them these new concepts.