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Name: ____________________________________ Date: __________________________ Geometry Unit 1 Day 3: Unknown Angles in Transversals and Parallel Lines Goal: I can use angle pairs in HW: Upcoming Events: parallel lines to find missing 1-3 Transversal Angles angles. Directions: Use your Unit 1 Reference Guide to help you answers the questions below. 1) Use the diagram below to find the measure of β πͺπΆπ. π¨π© and πͺπ« are straight lines. a) 30 b) 90 c) 52 d) 96 2) In the diagram above which is a pair of vertical angles? a) β COF & β EOD b) β AOF & β FOB c) β AOC & β DOB d) β AOE & β DOF 3) Which of the following represents a same side interior angle pair with the 48° angle? a) b) c) d) Use the diagram and work below to answer questions 4 & 5. Statements Reasons y + x + y β x = 180 #4 y = 90 2x = y β x Angles on a line equal 180 Combine Like Terms Division #5 2x = 90 β x Substitution 3x = 90 Addition x = 30 Division 4) What statement best fills in the blank labeled #4? a) 2y = 180 b) 2y β 2x = 180 c) 2y = 90 5) Which reason best fills in the blank labeled #5? a) Subtraction b) Angles around a point = 360 c) Vertical angles are congruent d) Angles on a line = 180 d) y = 90 Name: ____________________________________ Date: __________________________ Geometry Unit 1 Day 3: Unknown Angles in Transversals and Parallel Lines Discussion Given a pair of lines π΄π΅ and πΆπ· in a plane (see the diagrams 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: ο§ Corresponding Angles (corr.) are equal βͺ Same Side Interior Angles (ss. Int.) add to 180° Angle Pairs:____________________________ ο§ Alternate Exterior Angles (alt. ext.) are equal Angle Pairs:____________________________ ο§ Alternate Interior Angles (alt. int.) are equal Angle Pairs:____________________________ Angle Pairs:____________________________ ο§ Vertical Angles (Vert.) are equal Angle Pairs:_________________________________________ An _________________________________is sometimes useful when solving for unknown angles. In this figure, we can use the dotted auxiliary line to find the measures of β π and β π . Then we can use β π and β π to find the measure of β π. * Use your βZβs to find the alternate interior angles. Statements Reasons Exercises: Show work by CLEARLY labeling all angles in the diagram to find the missing angles. Make sure to draw in the auxiliary line and highlight your βZsβ 1. β π = _________ 2. An architect is inputting measurements into design software of an existing building. The shaded region is not accessible to measure. How can the architect determine the measure of angle i? β π = __________ 3. β π = _______ 4. β π = _______ β π = _______ 5. β π = __________ 6. β π = ________ 7. β π = ______ β π = ______ 8. β π = ________ Name: ____________________________________ Date: __________________________ Geometry A U2D7: Transversal Angles HOMEWORK 1-2 In each exercise below, find the unknown (labeled) angles. Give reasons for your solutions. 1. Statements Reasons If lines are parallel alternate exterior angles are equal. c + 53 = 180 β a = 53° 2. Statements Reasons β m = β j = j + k + 46 = 180 Substitution Directions: Show work by CLEARLY labeling all angles in the diagram to find the missing angles. Make sure to draw in the auxiliary line and highlight your βZsβ 3. β π = ___________ 4. β π = ____________ β π = ___________ 5. β β = __________ 6. β π = ________ β π = ________ Directions: Set up an equation to solve each problem below. S R 7. 3d - 24 12c β 8 U & 2d + 4 3c + 19 Y V V Find W X 8. Z T = ______ & = ______ & = ______ Find = _______ & = ______ & = _______ = _______ & = ______