Transcript Lesson 7x
Geometry- Lesson 7 Solve for Unknown AnglesTransversals Essential Question β’ Review of previously learned Geometry Facts β’ Practice citing the geometric justifications for future work with unknown angle proofs This lesson focuses on Transversals. What have you learned previously about transversals? Opening Exercise Use the diagram at the right to determine π₯ and π¦. π΄π΅ and πΆπ· are straight lines. 30Λ π₯ = ________ 52Λ π¦ = ________ Name a pair of vertical angles: β π¨πΆπͺ, β π«πΆπ© _____________________ Find the measure of β π΅ππΉ. Justify your calculation. β π©πΆπ= ππ° ___________________________ s on a line ___________________________ Discussion (5 min) Angle Facts 1. If two lines are cut by a transversal and corresponding angles are equal, then the lines are parallel. 1. If parallel lines are cut by a transversal, corresponding angles are equal. (This second part is often called the Parallel Postulate. It tells us a property that parallel lines have. The property cannot be deduced from the definition of parallel lines.) Given a pair of lines π΄π΅ and πΆπ· in a plane (see the diagram below), a third line πΈπΉ is called a transversal if it intersects π΄π΅ at a single point and intersects πΆπ· at a single but different point. The two lines π΄π΅ and πΆπ· are parallel if and only if the following types of angle pairs are congruent or supplementary β’ Corresponding Angles are equal in measure Abbreviation: ________ corr. s a and e , d and h, etc. __________________________ β’ Alternate Interior Angles are equal in measure alt. s Abbreviation: ________ c and f , d and e. __________________________ β’ Same Side Interior Angles are supplementary int. s Abbreviation: ________ c and e , d and f. ___________________________ Examples (8 min) Do Examples on your own 48Λ β π = _____ 132Λ β b = _____ 48Λ β c = _____ 48Λ β d = _____ auxiliary line e. 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? π= ππ° π= ππ° ππ° β πΎ = ______ Relevant Vocabulary Alternate Interior Angles: Let line π be a transversal to lines πΏ and π such that π intersects πΏ at point π and intersects π at point π. Let π be a point on πΏ, and π be a point on π such that the points π and π lie in opposite half-planes of π. Then the angle β π ππ and the angle β πππ are called alternate interior angles of the transversal π with respect to π and πΏ. Corresponding Angles: Let line π be a transversal to lines πΏ 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. Exercises Spend some time on your own or with a partner working on the following exercises. 1. 53° , ____________ corr. s β π = ______ 53° , ____________ vert. s β b = ______ int. s 127° , ____________ β c = ______ 2. 145° , ____________ s on a line β d = ______ alt. s 3. 54° , ____________ β e = ______ alt. s 68° , ____________ vert. s β f = ______ int. s 4. 92° , ____________ vert. s β g = ______ int. s 5. 100° , ____________ int. s β h = ______ 6. 114° , ____________ s on a line β i = ______ alt. s 7. 92° , ____________ alt. s β j = ______ 42° , ____________ s on a line β k = ______ 46° , ____________ alt. s β m = ______ 8. 81° , ____________ corr. s β n = ______ 9. 18° , ____________ s on a line β p = ______ 94° , ____________ corr. s β q = ______ 10. 46° , ____________ int. s β r = ______ alt. s Exit Ticket Find x, y and z 40° π₯ = ______ 113° π¦ = ______ 67° z = ________ Donβt Forget Problem Set!!!