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Lesson 2.6 Parallel Lines cut by a Transversal

Lesson 2.6 Parallel Lines cut by a Transversal. HW: 2.6/ 1-10, 14-16 Quiz 2.5 -2.6 Wednesday. Investigations for Lesson 2.6. Tools: protractor, straightedge, patty paper

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Lesson 2.6 Parallel Lines cut by a Transversal

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  1. Lesson 2.6 Parallel Lines cut by a Transversal HW: 2.6/ 1-10, 14-16 Quiz 2.5 -2.6 Wednesday

  2. Investigations for Lesson 2.6 Tools: protractor, straightedge, patty paper Objective: Discover relationships between special pairs of angles created by a pair of parallel lines cut by a transversal. Lesson 2.6 Special Angles on Parallel Lines Complete Investigations 1 & 2 WS Complete conjectures

  3. Parallel Lines and Transversals What You'll Learn You will learn to identify the relationships among pairs of interior and exterior angles formed by two parallel linesand a transversal.

  4. Parallel Lines and Transversals A l m B is an example of a transversal. It intercepts lines land m. In geometry, a line, line segment, or ray that intersects two or more lines at different points is called a __________ transversal 2 1 4 3 5 6 8 7 Note all of the different angles formed at the points of intersection.

  5. Parallel Lines and Transversals Parallel Lines Nonparallel Lines b l 2 1 2 1 3 4 4 3 m c 6 5 6 5 8 7 7 8 t r t is a transversal for land m. ris a transversal for b and c. The lines cut by a transversal may or may not be parallel.

  6. Parallel Lines and Transversals Exterior Interior Exterior Two lines divide the plane into three regions. The region between the lines is referred to as the interior. The two regions not between the lines is referred to as the exterior.

  7. Parallel Lines and Transversals l 2 1 4 3 m 6 5 8 7 When a transversal intersects two lines, _____ angles are formed. eight These angles are given special names. t Alternate angleslie on opposite sides of the transversal Same Side angles lie on the same side of the transversal Exterior angles lie outside the two lines. Interior angles lie between the two lines. Alternate Exterior anglesare on the opposite sides of the transversal, outside the lines. Alternate Interior anglesare on the opposite sides of the transversal, between the lines. Same Side Exterior anglesare on the same side of the transversal , outside the lines. Same Side Interior anglesare on the same side of the transversal, between the lines.

  8. Parallel Lines and Transversals congruent 2 1 4 3 6 5 7 8

  9. Parallel Lines and Transversals 2 1 4 3 6 5 8 7 supplementary

  10. Parallel Lines and Transversals 2 1 4 3 6 5 8 7 supplementary

  11. Parallel Lines and Transversals 2 1 4 3 6 5 8 7 congruent

  12. Parallel Lines and Transversals congruent

  13. Parallel Lines w/a transversal AND Angle Pair Relationships Types of angle pairs formed when a transversal cuts two parallel lines. alternate interior angles- AIA same side interior angles- SSI same side exterior angles- SSE alternate exterior angles- AEA linear pair of angles- LP corresponding angles - CA vertical angles- VA

  14. Vertical Angles = opposite angles formed by intersecting linesVertical angles are ALWAYS equal, whether you have parallel lines or not. Vertical angles are congruent.

  15. Angles forming a Linear Pair Linear Pair of Angles = Adjacent Supplementary Anglesmeasures are supplementary If two angles form a linear pair, they are supplementary.

  16. Parallel Lines and Transversals s t c 1 3 4 2 5 6 7 8 9 12 11 d 10 14 13 15 16 s || t and c || d. Name all the angles that are congruent to 1. Give a reason for each answer. corresponding angles 3  1 vertical angles 6  1 alternate exterior angles 8  1 corresponding angles 9  1 alternate exterior angles 14  1 same side exterior angles 1  4 alternate interior angles 5  10

  17. Parallel Lines and Transversals 1 2 3 4 6 5 7 8 Let’s Practice m<1=120° Find all the remaining angle measures. 60° 120° 120° 60° 120° 60° 120° 60°

  18. Parallel Lines and Transversals Another practice problem Find all the missing angle measures, and name the postulate or theorem that gives us permission to make our statements. 40° 180-(40+60)= 80° 60° 80° 60° 40° 80° 120° 100° 60° 80° 120° 60° 100°

  19. 1 2 3 4 6 5 7 8 SUMMARY: WHEN THE LINES ARE PARALLEL ♥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 Exterior Interior Exterior If the lines are not parallel, these angle relationships DO NOT EXIST.

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