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Lesson 4 COMMON CORE MATHEMATICS CURRICULUM U2 GEOMETRY Name_______________________ Date__________ Lesson 4: Solve for Unknown AnglesโTransversals Classwork Opening Exercise Use the diagram at the right to determine ๐ฅ and ๐ฆ. ๐ด๐ต and ๐ถ๐ท are straight lines. ๐ฅ = ________ ๐ฆ = ________ Name a pair of vertical angles: _____________________ Find the measure of โ ๐ต๐๐น. Justify your calculation. _____________________________________________________ _____________________________________________________ Discussion Given a pair of lines ๐ด๐ต and ๐ถ๐ท in a plane (see the diagram below), a third line ๐ธ๐น is called a transversal if it intersects ๐ด๐ต at a single point and intersects ๐ถ๐ท at a single but different point. The two lines ๐ด๐ต and ๐ถ๐ท are parallel if and only if the following types of angle pairs are congruent or supplementary: ๏ง Corresponding Angles are equal in measure _____________________________________ ๏ง Alternate Interior Angles are equal in measure _____________________________________ ๏ง Same Side Interior Angles are supplementary _____________________________________ Lesson 4 Solve for Unknown AnglesโTransversals 1 Lesson 4 COMMON CORE MATHEMATICS CURRICULUM U2 GEOMETRY Relevant Vocabulary Alternate Interior Angles: Let line ๐ be a transversal to lines ๐ฟ and ๐ such that ๐ intersects ๐ฟ at point ๐ and intersects ๐ at point ๐. Let ๐ be a point on ๐ฟ, and ๐ be a point on ๐ such that the points ๐ and ๐ lie in opposite halfplanes of ๐. Then the angle โ ๐ ๐๐ and the angle โ ๐๐๐ are called alternate interior angles of the transversal ๐ with respect to ๐ and ๐ฟ. Corresponding Angles: Let line ๐ be a transversal to lines ๐ฟ and ๐. If โ ๐ฅ and โ ๐ฆ are alternate interior angles, and โ ๐ฆ and โ ๐ง are vertical angles, then โ ๐ฅ and โ ๐ง are corresponding angles. Sketch this: Examples a. b. โ ๐ = ________ Relationship_______________________ Lesson 4 โ ๐ = ________ Relationship___________________ Solve for Unknown AnglesโTransversals 2 Lesson 4 COMMON CORE MATHEMATICS CURRICULUM U2 GEOMETRY c. d. โ ๐ = ________ Relationship_______________________ e. An AUXILARY โ ๐ = ________ Relationship___________________ LINE is sometimes useful when solving for unknown angles. In this figure, we can use the auxiliary line to find the measures of โ ๐ and โ ๐ (how?), then add the two measures together to find the measure of โ ๐. What is the measure of โ ๐? Exercises In each exercise below, find the unknown (labeled) angles. Give reasons for your solutions. โ ๐ = ____________________ 1. โ ๐ = ________________________ โ ๐ = ________________________ Lesson 4 Solve for Unknown AnglesโTransversals 3 Lesson 4 COMMON CORE MATHEMATICS CURRICULUM U2 GEOMETRY 2. โ ๐ = ________________________ โ ๐ = ________________________ 3. โ ๐ = ________________________ 4. โ ๐ = ________________________ Lesson 4 Solve for Unknown AnglesโTransversals 4 Lesson 4 COMMON CORE MATHEMATICS CURRICULUM U2 GEOMETRY 5. โ โ = ________________________ 6. โ ๐ = ________________________ 7. โ ๐ = ________________________ โ ๐ = ________________________ โ ๐ = _______________________ 8. โ ๐ = ________________________ Lesson 4 Solve for Unknown AnglesโTransversals 5 Lesson 4 COMMON CORE MATHEMATICS CURRICULUM U2 GEOMETRY โ ๐ = 9. ________________________ โ ๐ = ________________________ 10. โ ๐ = ________________________ Extra Credit (5 extra points per problem on the packet score) Find the unknown (labeled) angles. Give reasons for your solutions. 1. โ ๐ = ________________________ Lesson 4 Solve for Unknown AnglesโTransversals 6 COMMON CORE MATHEMATICS CURRICULUM Lesson 4 U2 GEOMETRY 2. โ ๐ = ________________________ โ ๐ = ________________________ 3. โ ๐ = ________________________ โ ๐ = ________________________ 4. โ ๐ = ________________________ Lesson 4 Solve for Unknown AnglesโTransversals 7