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Parallel Lines, Transversals, & Special Angle Pairs

Parallel Lines, Transversals, & Special Angle Pairs. When 2 lines intersect crazy, wonderful things happen!. 1. When 2 lines, rays or segments intersect, 4 angles are created. 4. 2. 3. Angles 1 & 4 are a linear pair = 180° Angles 1 & 2 are a linear pair = 180°

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Parallel Lines, Transversals, & Special Angle Pairs

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  1. Parallel Lines,Transversals, &Special Angle Pairs

  2. When 2 lines intersectcrazy, wonderfulthings happen!

  3. 1 When 2 lines, rays or segments intersect, 4 angles are created. 4 2 3 Angles 1 & 4 are a linear pair = 180° Angles 1 & 2 are a linear pair = 180° Angles 2 & 3 are a linear pair = 180° Angles 3 & 4 are a linear pair = 180° Angles 1 & 3 are VERTICAL ANGLES and are congruent. Angles 4 & 2 are VERTICAL ANGLES and are congruent.

  4. Non-Parallel lines Transversal A line, ray, or segment that intersects 2 or more COPLANAR lines, rays, or segments. Parallel lines transversal transversal

  5. exterior interior exterior INTERIOR –The space INSIDE the 2 lines EXTERIOR -The space OUTSIDE the 2 lines

  6. 1 2 3 4 5 6 7 8 Special Angle Relationships Interior Angles <3 & <6 are Alternate Interior angles <4 & <5 are Alternate Interior angles <3 & <5 are Same Side Interior angles <4 & <6 are Same Side Interior angles Exterior Angles <1 & <8 are Alternate Exterior angles <2 & <7 are Alternate Exterior angles <1 & <7 are Same Side Exterior angles <2 & <8 are Same Side Exterior angles Corresponding Angles Angles that are in the same position on both lines <1 & <5 are Corresponding angles <2 & <6 are Corresponding angles <3 & <7 are Corresponding angles <4 & <8 are Corresponding angles

  7. $ $ Let’s PracticeNaming Angle Pairs Name a pair of alternate interior angles Name a pair of same side exterior angles Name a pair of same side interior angles Name a pair of alternate exterior angles Name a linear pair Name a pair of vertical angles Name a pair of corresponding angles Name another pair of corresponding angles Name a linear pair Name a pair of vertical angles 2 1 4 3 5 6 7 8

  8. 1 2 3 4 6 5 7 8 If the lines are not parallel, these measurement relationships DO NOT EXIST. Special Angle MeasurementRelationshipsWHEN THE LINES ARE PARALLEL Check out the new notation. This extra set of arrows indicates parallel lines. ♥Alternate Interior Angles are CONGRUENT ♥Alternate Exterior Angles are CONGRUENT ♥Same Side Interior Angles are SUPPLEMENTARY ♥Same Side Exterior Angles are SUPPLEMENTARY • Corresponding angles are CONGRUENT

  9. Let’s look closer 1 2 2 1 3 4 4 3 5 6 When lines are parallel, measurement relationships exist. 5 6 8 7 7 8 When lines are not parallel, special angle pairs do not have a measurement relationship. Either way, special angle pairs keep the same names.

  10. Let’s Practice m<1=120° Find all the remaining angle measures AND give the name of the special angle pair. 120° 60° 120° 60° m<1=91° Find all the remaining angle measures AND give the name of the special angle pair. 2 1 120° 60° 4 3 120° 60° 89° 91° 5 6 91° 89° 7 8 WE DON’T KNOW! 1 2 3 4 6 5 7 8

  11. Vocabulary Parallel lines: Lines that are always equidistant from each other – they will never intersect. (2D or 3D) Perpendicular lines: Lines that intersect at a 90◦angle. (2D or 3D) Skew lines: Lines that are not parallel but will never intersect. (3D only)

  12. Use the diagram to name each of the following. • A pair of parallel planes • All lines that are parallel to 3. Four lines that are skew to 4. All lines that are parallel to plane QUV 5. A plane parallel to plane QUW

  13. Identify all pairs of each type of angle in the diagram below right. • Correspondingangles • Same-sideinteriorangles • Alternateinteriorangles • Alternateexteriorangles

  14. Find the value of x and y. Then find the measure of each labeled angle. • What kind of angles are these? • What is their measurement relationship? • How shall we set up the equation? • Do it. Angle measures are 103 ◦ and 77◦ x + x – 26 = 180 2x = 206 x = 103 Are we done?

  15. Another practice problem Find all the missing angle measures, and name the postulate or theorem that gives us permission to make our statements. 40° 120°

  16. Assignment Practice 3.1 and 3.2

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