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Do Now

Do Now. Name the type(s) of angles pairs in each diagram. 2. 2. 3. Properties of Parallel Lines and Transversals. Parallel Lines. Recall: Parallel lines are coplanar lines that DO NOT intersect. Think Pair Share.

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Do Now

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  1. Do Now • Name the type(s) of angles pairs in each diagram. • 2. 2. 3.

  2. Properties of Parallel Linesand Transversals

  3. Parallel Lines • Recall: Parallel lines are coplanar lines that DO NOTintersect

  4. Think Pair Share -Think quietly for 1 minute about a word that has the prefix TRANS in it - Pair with a neighbor and tell them what you thought of -Share with the whole class

  5. Trans means… • Trans means across, through, or cross over • So what is a transversal line going to do?

  6. Transversals • A transversal is a line that crosses over or intersects 2 coplanar lines at distinct points • Real life examples? • Red and blue lines on paper, the corners of the walls, the ceiling, the floor, the desks, etc

  7. Parallel Lines cut by a Transversal in the Ben Franklin Bridge

  8. Special Angles • When the transversal cuts the 2 lines, it forms 8 angles • Luckily for us, only 2 unique angle measures are formed! Which <s are congruent??

  9. Have at it • Using what you’ve learned so far, can you figure out what the measure is for angles 1, 2 and 3? 1 50 2 3 5 4 6 7

  10. Corresponding Angles • Corresponding angles lie on the same side of the transversal and in corresponding positions • Corresponding angles are congruent when the transversal cuts across parallel lines • Ex: <1 and <6; <2 and <5; <4 and < 7; <3 and <8 1 2 3 4 5 6 7 8

  11. Alternate Exterior Angles • Alternate exterior angles are outside the two lines on opposite sides of the transversal • Alternate exterior angles are congruent when the transversal cuts across parallel lines • Ex: <1 and <8; <2 and <7 1 2 3 4 5 6 7 8

  12. Alternate Interior Angles • Alternate interior angles are between the two lines on opposite sides of the transversal • Alternate interior angles are congruent when the transversal cuts across parallel lines • Ex: <4 and <5; <6 and <3 1 2 3 4 5 6 7 8

  13. Same-side Interior Angles • Same-side interior angles are between the parallel lines on the same side of the transversal • Same-side interior angles are supplementary when the transversal cuts across parallel lines Ex: <4 and <6 <3 and <5 1 2 3 4 5 6 7 8

  14. Proof: Prove ∠3 and ∠ 5 are supplementary angles Given: Lines a and b are parallel a b • Given • Definition of linear pair • If ∠2 and ∠3 are a linear pair, then they are supplementary • Definition of corresponding angles • If ∠2 and ∠5 are corresponding, then they are congruent • If ∠2  ∠5, then m∠2 = m∠5 • If ∠2 and ∠3 are supplementary and m∠2 =m∠5, then ∠5 and ∠3 are also supplementary • Lines a and b are parallel lines • ∠2 and ∠3 are a linear pair • ∠2 and ∠3 are supplementary • ∠2 and ∠5 are corresponding • ∠2  ∠5 • m∠2 = m∠5 • ∠5 and ∠3 are supplementary 1 2 4 3 6 5 7 8

  15. Identify the following pairs of angles as corresponding, vertical, alternate-interior, alternate-exterior, or same-side interior 1. ∠1 and ∠3 2. ∠3 and ∠6 3. ∠11 and ∠5 4. ∠4 and ∠6 5. ∠11 and ∠9

  16. r//s and m ∠3 = 78°. Find the measure of each angle. ∠1 = ∠2 = ∠4 = ∠5 = ∠6 = ∠7 = ∠8 = 102 78 102 102 78 78 102

  17. l//m Find x. 3x + 4 + 94 = 180 3x + 98 = 180 3x = 82 x = 27.3 3x + 4 94

  18. Given n//m, m<2 = 3x + 4 and m<8 = 2x + 10. Find x then find m<4 3x + 4 3x + 4 = 2x + 10 x = 6 m<4 = m<2 m<4 = 3x+4 =3(6) + 4 M<4 = 22 2x + 10

  19. Exit Ticket 1 2 3 • m<1 = 50°. Find m<2 and m<3. • Find y. 7y - 13 3y -7

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