Parallel and Perpendicular Lines Complete the WAM 11

Parallel and Perpendicular Lines Complete the WAM 11 -15 Homework Questions? ? ?

Parallel and Perpendicular Lines Dance Transversal Congruent (equal) or Supplementary (add up to 180 degrees) • • • Vertical angles Corresponding angles Same - side interior angles Alternate exterior angles Same- side exterior angles Alternate interior angles

Parallel and Perpendicular Lines Caution! You cannot tell if angles are congruent by measuring because measurement is not exact.

Parallel and Perpendicular Lines Additional Example 1 Continued Angles circled in blue appear to be congruent to each other, and angles circled in red appear to be congruent to each other. 1 @ 3 @ 5 @ 7 2 @ 4 @ 6 @ 8

Parallel and Perpendicular Lines Check It Out: Example 1 Measure the angles formed by the transversal and parallel lines. Which angles seem to be congruent? 1 2 3 4 5 6 7 8 1, 4, 5, and 8 all measure 36° and appear to be congruent. 2, 3, 6, and 7 all measure 144° and appear to be congruent.

Parallel and Perpendicular Lines Check It Out: Example 1 Continued Angles marked in blue appear to be congruent to each other, and angles marked in red appear to be congruent to each other. 1 @ 4 @ 5 @ 8 2 @ 3 @ 6 @ 7 1 2 3 4 5 6 7 8

Parallel and Perpendicular Lines Some pairs of the eight angles formed by two parallel lines and a transversal have special names.

Parallel and Perpendicular Lines

Parallel and Perpendicular Lines Check It Out: Example 2 A In the figure, line n || line m. Find the measure of the angle. The 144 angle and 7 are alternate exterior angles. 1 144° m m 7 = 144° 3 4 5 6 n 8 7 7

Parallel and Perpendicular Lines Check It Out: Example 2 B In the figure, line n || line m. Find the measure of the angle. 1 1 is supplementary to the 144° angle. m 1 + 144° = 180° – 144° m 1 = 36° 1 144° 3 4 5 6 7 8 m n

Parallel and Perpendicular Lines Check It Out: Example 2 C In the figure, line n || line m. Find the measure of the angle. 5 5 and 1 are corresponding angles. m 5 = 36° 1 144° 3 4 5 6 7 8 m n

Parallel and Perpendicular Lines Lesson Quiz for Student Response Systems 1. In the figure, x || y. Identify the angles congruent to 3. A. 1, 2, 4 B. 2, 4, 6 C. 4, 5, 6 D. 1, 5, 8

Parallel and Perpendicular Lines Lesson Quiz for Student Response Systems 2. In the figure, x || y. If m 5 = 115°, what is m 7? A. 25° B. 65° C. 75° D. 115°

Parallel and Perpendicular Lines Solve for x and then find the angle measurements. 2 xº 2 x = 5 x – 108 = 3 x 36 = x (5 x -108)º 2(36) = 72º 5(36) – 108 = 72º

Parallel and Perpendicular Lines 180 Rule for Triangles - the sum of the interior angles of any triangle is always 180. b 80 40 a 40 x c + 80 + x = 180 120 + x = 180 x = 60

Parallel and Perpendicular Lines Find each angle below. 2 y - 10 y + 14 = 63 2 y - 10 = 88 y - 20 = 29 y+14 y - 20 180 (y + 14) + (2 y - 10) + (y - 20) = 180 4 y - 16 = 180 +16 4 y = 196 y = 49

Parallel and Perpendicular Lines Find the measure of each marked angle below. (x + 70)° (3 x – 80)° Alternate interior angles. x + 70 = 3 x – 80 2 x = 150 x = 75 x + 70 = 75 + 70 = 145°

Parallel and Perpendicular Lines Find the measure of each marked angle below. (4 x – 45)° (2 x – 21)° Same Side Interior angles. 4 x – 45 + 2 x – 21 = 180 6 x – 66 = 180 6 x = 246 x = 41 4(41) – 45 164 – 45 2(41) – 21 82 – 21 119 ° 61 ° 180 – 119 = 61°

Parallel and Perpendicular Lines el l l a r a p y db e t a e r c s r pai ich h e l w g n n i a a l y f p ex enti d d n i a n l a a c s I r * * tary ve n s e n a m r e t l a p up by s t r u o c t s n e e n u i l ngr o c e r a s r angle pai and why. 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. üIndependent Practice IXL üFinish Packet with Vocabulary http: //bit. do/anglerelationships 102 http: //bit. do/anglerelat

Parallel and Perpendicular Lines Additional Practice http: //bit. do/AAgame I can identify angle pairs created by parallel lines cut by a transversal and explain which angle pairs are congruent or supplementary and why. http: //bit. do/AAreviewgames