* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download PPT 2.6 Special Angles on Parallel Lines
Riemannian connection on a surface wikipedia , lookup
Technical drawing wikipedia , lookup
Rotation formalisms in three dimensions wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Perspective (graphical) wikipedia , lookup
History of trigonometry wikipedia , lookup
Integer triangle wikipedia , lookup
Line (geometry) wikipedia , lookup
Compass-and-straightedge construction wikipedia , lookup
Multilateration wikipedia , lookup
Rational trigonometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
Warm-Up 2.6 Parallel Line Angles Objective Explore relationships of the angles formed by a transversal cutting parallel lines. HW: p. 141 #1, 3-6, 9-10 (DUE Tuesday 9/29) Investigation “Which angles are congruent?” Step 1) Using a ruler, draw a pair of parallel lines on your paper. Step 2) Draw a line that intersects both parallel lines (a transversal). Step 3) Label the Angles 1-8 1 3 5 7 6 8 2 4 Step 4) Place the patty paper over angles 1-4 and trace the intersecting lines and the four angles. 1 3 2 4 Step 5) Slide the patty paper down to angles 5-8. What do you notice? 1 3 2 4 Transveral Special Angles on Parallel Lines Keyword Conjecture Sketch Corresponding Angles (CA) congruent Corresponding Angles are ___________. Alternate Interior Angles (AIA) congruent Alternate Interior angles are __________. 1 8 1 3 4 6 5 7 Alternate Exterior Angles (AEA) 3 4 6 5 7 8 congruent Alternate Exterior angles are _________. 1 3 4 6 5 7 8 2 2 2 Special Angles on Parallel Lines Keyword Conjecture Consecutive Interior Angles Same Side Interior Angles are _______________. supplementary Consecutive Exterior Angles Same side exterior angles supplementary are ______________. Sketch 1 8 1 7 2 3 4 6 5 Parallel lines Conjecture 3 4 6 5 7 2 8 If two parallel lines are cut by a transversal, then corresponding angles are ____________, congruent alternate interior angles are ______________, and alternate congruent congruent exterior angles are ________________. Special Angles on Parallel Lines Converse of Parallel Lines Conjecture If 2 lines are cut by a transversal to form pairs of congruent Corresponding Angles, congruent Alternate Interior Angles, congruent Alternate Exterior Angles, supplementary Consecutive interior angles, or supplementary exterior angles, parallel then the lines are ________________. BASICALLY: IF ALL THE ANGLS ARE CONGRUENT, THEN THE LINES ARE PARALLEL Practice Time! 1) Find the missing angle. ?° 36° 1) Find the missing angle. ?° 36° 90 ° – 36 = 54° 2) Find the missing angle. ?° 64° 2) Find the missing angle. ?° 64° 90 ° – 64° = 26° 3) Solve for x. 2x° 3x° 3) Solve for x. 2x° 3x° 3x° + 2x° = 90° 5x = 90 x =18 4) Solve for x. x + 25 2x + 5 4) Solve for x. x + 25 2x + 5 (2x + 5) + (x + 25) = 90 3x + 30 = 90 3x = 60 x = 20 5) Find the missing angle. ?° 168° 5) Find the missing angle. ?° 180° – 168° = 12° 168° 6) Find the missing angle. 58° ?° 6) Find the missing angle. 58° 180° – 58° = 122° ?° 7) Solve for x. 4x 5x 7) Solve for x. 4x 4x + 5x = 180 9x = 180 x = 20 5x 8) Solve for x. 2x + 10 3x + 20 8) Solve for x. 2x + 10 3x + 20 (2x + 10) + (3x + 20) = 180 5x + 30 = 180 5x = 150 x = 30 9) Lines l and m are parallel. l||m Find the missing angles. 42° a° c° b° d° e° g° f° l m 9) Lines l and m are parallel. l||m Find the missing angles. 42° 138° 138° 42° 42° 138° 138° 42° l m 10) Lines l and m are parallel. l||m Find the missing angles. 81° a° c° b° d° e° g° f° l m 10) Lines l and m are parallel. l||m Find the missing angles. 81° 99° 99° 81° 81° 99° 99° 81° l m x + (2x + 45) = 180 3x + 45 = 180 3x = 135 x = 45 11) Find the missing angles. 70 ° 70 ° b° Hint: The 3 angles in a triangle sum to 180°. d° 65 ° 11) Find the missing angles. 70 ° 70 ° 40° Hint: The 3 angles in a triangle sum to 180°. 75 ° 65 ° 12) Find the missing angles. 45 ° 50 ° b° Hint: The 3 angles in a triangle sum to 180°. d° 75 ° 12) Find the missing angles. 45 ° 50 ° 85° Hint: The 3 angles in a triangle sum to 180°. 20° 75 ° In the figure a || b. 13. Name the angles congruent to 3. 1, 5, 7 14. Name all the angles supplementary to 6. 1, 3, 5, 7 15. If m1 = 105° what is m3? 105° 16. If m5 = 120° what is m2? 60° The End Exit Ticket 2.6 s k i d c j g 64 a b h 108 f e 75 m p 79 n 169 q t 61