In this lesson, students will learn how to find missing angle measures with parallel lines using angle pairs. Students will start by reviewing linear pairs and vertical angles. Then, students will learn how parallel lines cut by a transversal form corresponding angles. Students will use this new information to find missing angle measures with parallel lines using angle pairs. You can expect this lesson with additional practice to take one `45`-minute class period.
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Students will be able to find missing angle measures with parallel lines using angle pairs.
Start the lesson by reviewing linear pairs and vertical angles with students.
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Give students a few minutes to try and identify two different sets of linear pairs and vertical angles. It may be beneficial to allow students to discuss and share their ideas as well before reviewing the information as a class. Students should be able to identify additional sets of linear pairs and vertical angles if needed, and they should also recognize the relationship between the angles for each type.
It is important for students to understand that they cannot assume lines are parallel. You will want to explicitly point out these red parallel line markers, and let students know that they have to have the same markers in order for lines to be parallel. This will also be students’ first time seeing “transversal”, so make sure to give them the definition: a line that crosses (intersects) two or more other lines.
You can let students know that corresponding angles can help them find many other angle pairs. Show students how the angles formed with one parallel line can “slide” on the transversal to the other parallel line. Students should be able to identify which angle would be an exact copy of `\angle 1`, as well as which angles would be congruent to `\angle 2`, `\angle 3`, and `\angle 4`. Although student responses may not use the new vocabulary, it will be helpful to use vocabulary like “congruent”, “transversal”, and “corresponding angles” when going over the new information.
Before moving on, make sure students understand corresponding angles are congruent and are able to identify corresponding angle pairs with the image shown. One way of checking student understanding is to pose “What if” questions, like “What would the measure of `\angle 6` be if `\angle 2` was `72^\circ`?”
Students will use their review from the warm up and the new knowledge of corresponding angles to find the pattern. Give students a few minutes to work with a partner or table group to problem solve and try to find the missing angle measures. Once students have their angle measures, consider asking students what they noticed about their answers. Help students to recognize that the angle measures in this diagram are always either `50^\circ` or `130^\circ`.
Ask students to explain how they approached finding the missing angle measures as well. Although students may have used different approaches, they ultimately would have needed to use corresponding angles at least once to find all of the missing angle measures.
The purpose of this example is to focus students on a single angle pair instead of finding all of the angles.
Ask students to try to determine the measure of `\angle BCF` using what they know. For students who are struggling, consider asking them to identify an angle that would have the same measure as `\angle CFG`. Make sure to give students time to think through and process the problem before reviewing the answer.
To extend on this problem, ask students what `3` angles would have the same measure as `\angle BCF`.
Allow students time to attempt this problem with a partner. Ideally, students should be able to recognize corresponding angle pairs more easily to help them determine if the given angles are congruent or form a linear pair. As students are working, circulate to listen for any misconceptions students may have.
To help check students’ understanding for finding missing angle measures with parallel lines using angle pairs, see if they are able to complete this quick review. Students should recognize that corresponding angles are always congruent. Encourage students to use the vocabulary; however, also accept it if students say “have equal measures”. Students should then be able to identify the angle measures for each angle in the image.
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 with parallel lines using angle pairs. Check out the online practice and assign to your students for classwork and/or homework!
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