Introduction to Angle Relationships Lesson Plan

Warm Up

Based on what students recall from `6`th grade, students should try to identify each type of angle and its measure. It may be helpful to let students know they can give a range for angle measures if needed. If students are unable to identify the angles as acute, obtuse, right, and straight, then they should at least be able to determine the angle measurements (or ranges of measurements).

Understanding notation with angles

When reviewing with students, stress the importance of naming the angles correctly by their vertices, like `∠JKL`. Students must recognize the importance of the square to indicate the right angle. Consider also asking students why they were told that `MO` formed a straight line and why it’s needed.

Complementary angles

To introduce the angle relationships, start with complementary angles. Give students an opportunity to look at the examples. Students should recognize that `∠ABD` forms a right angle, and ideally recognize that the second set of angles add up to `90^\circ`.

If students do not recognize that the angle pairs have a sum of `90^\circ`, then consider asking them to focus on the angle measures themselves. Help students recognize that complementary angles always have a sum of `90^\circ`. 

You should point out that complementary angles may or may not share a side.

Identifying measures complementary angles

To help students see the usefulness of understanding angle relationships, see if students are able to answer the question without prompting. Students should ideally recall that complementary angles add up to `90^\circ`. From there, they should be able to use their problem-solving skills to find the missing angle.

Expanding with complementary angles

To help expand on complementary angles, ask students to pick a random measure for an angle that could have a complement. Then, ask students to find the complementary angle to the angle they picked. For example, if a student chose `32^\circ`, then they would find that the complement is `58^\circ`. Have students share the angle pair they came up with to help students see the variety of potential combinations.

Supplementary Angles

Similar to complementary angles, ask students to look at two examples of supplementary angles and what they notice. 

Again, students should ideally recognize that the angle pairs add up to `180^\circ`. It can be helpful to remind students that the angles do not necessarily have to share a side to be supplementary.

Identifying measures of supplementary angles

To continue with angle relationships, see if students are able to answer the question without prompting. Students should recall that supplementary angles add up to `180^\circ`. From there, they should be able to use their problem-solving skills to find the missing angle.

Expanding with supplementary angles

Similar to the quick task for complementary angles, have students come up with one example of a supplementary angle pair. Encourage students to try and come up with unique combinations so that students can see some of the different combinations that are possible.

Using angle relationships without images

Students should be able to answer these questions based on what they know about complementary and supplementary angles; however, they may struggle more because they do not have the visual cues of the images. Give students time to complete the problems and check their work with a partner.

Memory trick for identifying angle pairs

You may notice that some students mix up the angle pair names with their sums. One easy way to help students remember, consider pointing out to students that `C` comes before `S` in the alphabet, just like `90` comes before `180` when counting. Because of this, complementary always has a sum of `90`, and supplementary always has a sum of `180`.