Lesson plan

In this lesson, students will learn how to find missing angle measures using parallel lines and triangles. Students will review concepts they should already know related to triangles and parallel lines. Then, students will be shown the new problem types and be given an opportunity to apply what they know to find the missing angle. You can expect this lesson with additional practice to take one `45`-minute class period.

Grade 8

Parallel Lines

8.G.A.5

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Students will be able to find missing angle measures using parallel lines and triangles.

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Start the lesson by reviewing the essential prerequisite skills for finding missing angle measures using parallel lines and triangles.

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In order to be successful in the lesson, students will need to know that triangle angles have a sum of `180^\circ`. Students will also need to know how to use parallel lines to find missing angle measures using angle pairs, like corresponding angles, vertical angles, and linear pairs.

Students will likely be surprised when they see this image; however, encourage them to identify at least `5` things they can tell from the image. This is intended to be exploratory for students, so what they identify could be anything that the students notice about the image, even if it is just identifying which lines are parallel.

It may help to have students write their lists on sticky notes or a piece of paper. Encourage students to review their list of known things with a partner or table group. As students share, it allows you to see what prior knowledge is automatically activated for students.

Some students may highlight the known angle measures, as well as which angle is the missing angle. When reviewing what students know, it may be helpful to ask students to think about whether the information could help them find the value of `x`. Ideally, through reviewing the information, the students will have highlighted most, if not all, of the information needed.

Most students will realize they have to find the measure of `\angle ADC` to find `x`. They may find the measure of `\angle ADC` using different methods. This can include recognizing `\angle DHG` and `\angle ADC` as corresponding angles. They may also choose to find the measure of `\angle HDC` since it is a same-side interior angle with `\angle DHG`. Then they can find the measure of `\angle ADC`. All of these methods are valid for finding the measure of `\angle ADC`. From there, students can use their knowledge of triangles to find the `x` equals `70`.

Similar to the previous example, ask students to think about what they notice in the image. It may be helpful for some students to write down their lists again.

Students should recognize the images are similar; however, the given angles have changed. As students are examining the image, ask students to also come up with a plan to try and find the value of `x`.

Show students again that they can use corresponding angles to find the measure of `\angle CDH`, which would be `96^\circ`. The difference in this example is we will have to subtract the measure of `\angle GHK` from `180` before we can find `x`.

It is important for you to be aware of misconceptions students may have.

- Because the lines are parallel, students will sometimes think that all of the angles are congruent, even if they are on different transversals; however, this is obviously not the case.
- Students may also misidentify whether the known angle outside of the triangle is congruent or supplementary to one of the interior triangle measures. In these situations, encourage the student to cover up any of the unnecessary lines or angles that make the image more confusing.

Similar to the previous example, this example contains an extra step. Here, encourage students to use corresponding angles to find the measure of `\angle BCG` first. Then you can remind students that vertical angles are congruent!

After you’ve completed the examples with the whole class, it’s time for some independent practice! ByteLearn gives you access to tons of practice problems for finding missing angle measures using parallel lines and triangles. Check out the online practice and assign to your students for classwork and/or homework! As students work, be sure to circulate to look for and address any misconceptions that may arise.

Finding Missing Angle Measures Using Parallel Lines and Triangles Practice

Problem 1 of 4

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