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Lesson 7 NYS COMMON CORE MATHEMATICS CURRICULUM M1 GEOMETRY Lesson 7: Solve for Unknown AnglesβTransversals Classwork Opening Exercise Use the diagram at the right to determine π₯ and π¦. β‘π΄π΅ and β‘πΆπ· are straight lines. π₯= π¦= Name a pair of vertical angles: Find the measure of β π΅ππΉ. Justify your calculation. Discussion Given line π΄π΅ and line πΆπ· in a plane (see the diagram below), a third line πΈπΉ is called a transversal if it intersects β‘π΄π΅ at a single point and intersects β‘πΆπ· at a single but different point. Line π΄π΅ and line πΆπ· are parallel if and only if the following types of angle pairs are congruent or supplementary. ο§ Corresponding angles are equal in measure ο§ Alternate interior angles are equal in measure ο§ Same side interior angles are supplementary Lesson 7: Date: Solve for Unknown AnglesβTransversals 4/29/17 © 2014 Common Core, Inc. Some rights reserved. commoncore.org S.39 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 7 NYS COMMON CORE MATHEMATICS CURRICULUM M1 GEOMETRY Examples 1. 2. mβ π = mβ π = 3. 4. mβ π = 5. mβ π = An _________________________________is sometimes useful when solving for unknown angles. In this figure, we can use the auxiliary line to find the measures of β π and β π (how?), then add the two measures together to find the measure of β π. What is the measure of β π? Lesson 7: Date: Solve for Unknown AnglesβTransversals 4/29/17 © 2014 Common Core, Inc. Some rights reserved. commoncore.org S.40 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 7 NYS COMMON CORE MATHEMATICS CURRICULUM M1 GEOMETRY Exercises In each exercise below, find the unknown (labeled) angles. Give reasons for your solutions. 1. mβ π = mβ π = mβ π = 2. mβ π = 3. mβ π = mβ π = 4. mβ π = 5. mβ β = 6. mβ π = Lesson 7: Date: Solve for Unknown AnglesβTransversals 4/29/17 © 2014 Common Core, Inc. Some rights reserved. commoncore.org S.41 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 7 NYS COMMON CORE MATHEMATICS CURRICULUM M1 GEOMETRY 7. mβ π = mβ π = mβ π= 8. mβ π = 9. mβ π = mβ π = 10. mβ π = Relevant Vocabulary Alternate Interior Angles: Let line π‘ be a transversal to lines π and π such that π‘ intersects π at point π and intersects π at point π. Let π be a point on line π and π be a point on line π such that the points π and π lie in opposite half-planes of π‘. Then β π ππ and β πππ are called alternate interior angles of the transversal π‘ with respect to line π and line π. Corresponding Angles: Let line π‘ be a transversal to lines π and π. If β π₯ and β π¦ are alternate interior angles, and β π¦ and β π§ are vertical angles, then β π₯ and β π§ are corresponding angles. Lesson 7: Date: Solve for Unknown AnglesβTransversals 4/29/17 © 2014 Common Core, Inc. Some rights reserved. commoncore.org S.42 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 7 NYS COMMON CORE MATHEMATICS CURRICULUM M1 GEOMETRY Problem Set Find the unknown (labeled) angles. Give reasons for your solutions. 1. mβ π = 2. mβ π = mβ π = 3. mβ π = mβ π = 4. mβ π = Lesson 7: Date: Solve for Unknown AnglesβTransversals 4/29/17 © 2014 Common Core, Inc. Some rights reserved. commoncore.org S.43 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.