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Geometry 71 Parallel Lines and Transversals BPW 3.5a.notebook Angles and Lines • Students will use parallel lines cut by a transversal to find angle measurements. • Students will use vertical angles to prove congruency. TEKs 8.8A Write onevariable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants 8.8C Model and solve onevariable equations with variables on both sides of the equal sign that represent mathematical and realworld problems using rational number coefficients and constants 8.8D Use informal arguments to establish facts about the angle sum and exterior angle of triangles, the angles created when parallel lines are cut by a transversal, and the angleangle criterion for similarity of triangle Geometry Butterflies, Pinwheels and Wallpaper Identify the coordinates of the new vertices after the transformations. (x,y) (x,y) 1. Parallelogram ABCD is rotated counterclockwise 90 o. Point A (4, 3) Point B (1, 3) Point C (0, 1) Point D (5 1) 2. Pentagon LMNOP is rotated 180 o. (x,y) (x,y) Point L(1, 3) Point M (3, 4) Point N (5, 3) Point O (4, 1) Point P (2, 1) answer 1. 2. 3. Triangle EFG is reflected across the xaxis and translated right 2 units. 3. Point E (3, 3) Point F (2, 5) Point G (0, 2) (x,y) (x+2,y) Title Page Warm Up Math Humor Two wrongs don’t make a right, 90o 180 Feb 2111:29 AM 90o o but two rights make a straight angle Math Humor Angles Parallel Lines and Transversal Help Section 1. Color the alternate interior and exterior angles 3 2. Color the consecutive interior and exterior angles Angles in Real Life 3. Color the corresponding angles four colors Introduction 7 1 2 4 5 6 8 Labsheet 1 Geometry 71 Parallel Lines and Transversals BPW 3.5a.notebook Properties of Transversals to Parallel Lines Cut and tape Labsheet in your journal 3.0 Vertical: 1&4; 2&3; 120 m<1=_____ m<2=_____ m<4=_____ Adjacent: 1&2; 2&4 m<5=_____ m<6=_____ Corresponding: 1&5 m<7=_____ m<8=_____ Complementary <AFB & <BFC <BFC & <EFD o Which angles are vertical? Which angles are adjacent? Which angles are corresponding? Name two pair of complementary & supplementary angles in the figure. <2, 3, 6 & 7 = 60o m<3=_____ 1 2 3 4 5 6 7 8 <1, 4, 5 & 8 = 120o Pull Find the following measures. C B 40o 90o 50o A F D 50o E Activity Labsheet Be a deep sea diver... or an astronaut? Find a friend and them what a transversal is. Friend Transition ______ Date Parallel Lines and Transversals 1. What is a • a line that intersects a set transversal? of parallel lines • Would You Rather? 2. What are • vertical angles opposite each vertical & other (always congruent) adjacent angles? • adjacent angles are side by side with common vertex adjacent forms 8 angles 2 • Alternate Angles (opposite) ~interior (inside) ~exterior (outside) • Consecutive Angles (same side) ~co-interior angles (inside) • Corresponding Angles letter v 1 3 4 vertical ~matching places Notes Notes 2 Geometry 71 Parallel Lines and Transversals BPW 3.5a.notebook 3. What are • complementary 2 angles complementary together equal 90o & supplementary angles? • supplementary 2 angles together equal 180o It is right to compliment someone! • do not have to be next to each other Activity Simon Says Play “Simon Says?” Have students work in groups of 4 & each group has 2 meter sticks. Use rules of “Simon Says” ask students to demonstrate: 1. 4. 7. 10. actute angle 2. supplementary angles 5. complementary angles 8. perpendicular lines 11. obtuse angle vertical angles right angle parallel lines 3. 6. 9. 12. straight angle adjacent angles intersecting lines skew lines 50o 40o 60o 120o Notes Activity Simon Says Practice Parallel Lines Worksheet Beautiful Homework Closing Questions Which angles are always congruent? (vertical) Which angles are next to one another? (adjacent) Closing Questions 3