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Understanding Angle Relationships in Parallel Lines and Transversals

Explore special angle relationships within parallel lines and transversals, covering interior and exterior angles, alternate angles, same-side angles, corresponding angles, vertical angles, and supplementary angles.

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Understanding Angle Relationships in Parallel Lines and Transversals

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  1. Parallel Lines & Transversals

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

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

  4. 1 2 3 4 5 6 7 8 Special Angle Relationships Interior Angles 3, 4, 5, 6 Alternate Interior Angles – <3 & <6 are Alternate Interior angles <4 & <5 are Alternate Interior angles

  5. 1 2 3 4 5 6 7 8 Special Angle Relationships Interior Angles 3, 4, 5, 6 Alternate Interior Angles – 3 & 6 are Alternate Interior angles 4 & 5 are Alternate Interior angles

  6. 1 2 3 4 5 6 7 8 Special Angle Relationships Interior Angles 3, 4, 5, 6 Alternate Interior Angles – 3 & 6 are Alternate Interior angles 4 & 5 are Alternate Interior angles

  7. 1 2 3 4 5 6 7 8 Special Angle Relationships Same-Side Interior Angles – 3 & 5 are Same Side Interior angles 4 & 6 are Same Side Interior angles

  8. 1 2 3 4 5 6 7 8 Special Angle Relationships Same-Side Interior Angles – 3 & 5 are Same Side Interior angles 4 & 6 are Same Side Interior angles

  9. 1 2 3 4 5 6 7 8 Special Angle Relationships • Exterior Angles 1, ∠ 2, ∠ 7, ∠ 8

  10. 1 2 3 4 5 6 7 8 Special Angle Relationships • Exterior Angles ∠ 1, ∠ 2, ∠ 7, ∠ 8

  11. 1 2 3 4 5 6 7 8 Special Angle Relationships • Exterior Angles ∠ 1, ∠ 2, ∠ 7, ∠ 8 Alternate Exterior Angles – ∠2 & ∠ 7 are Alternate Exterior angles ∠ 1 & ∠ 8 are Alternate Exterior angles

  12. 1 2 3 4 5 6 7 8 Special Angle Relationships • Exterior Angles ∠ 1, ∠ 2, ∠ 7, ∠ 8 Alternate Exterior Angles – ∠ 2 & ∠ 7 are Alternate Exterior angles ∠ 1 & ∠ 8 are Alternate Exterior angles

  13. 1 2 3 4 6 5 7 8 Special Angle Relationships Same-Side Exterior Angles – ∠ 1 & ∠ 7 are Same-Side Exterior angles ∠ 2 & ∠ 8 are Same-Side Exterior angles

  14. 1 2 3 4 6 5 7 8 Special Angle Relationships Same-Side Exterior Angles – ∠ 1 & ∠ 7 are Same-Side Exterior angles ∠ 2 & ∠ 8 are Same-Side Exterior angles

  15. 1 2 3 4 5 6 7 8 Special Angle Relationships Corresponding Angles: Angles that are in the same place ∠ 1 & ∠ 5 are Corresponding Angles ∠ 2 & ∠ 6 are Corresponding Angles ∠ 3 & ∠ 7 are Corresponding Angles ∠ 4 & ∠ 8 are Corresponding Angles

  16. 1 2 3 4 5 6 7 8 Special Angle Relationships Corresponding Angles: Angles that are in the same place ∠ 1 & ∠ 5 are Corresponding Angles ∠ 2 & ∠ 6 are Corresponding Angles ∠ 3 & ∠ 7 are Corresponding Angles ∠ 4 & ∠ 8 are Corresponding Angles

  17. 1 2 3 4 5 6 7 8 Special Angle Relationships Vertical Angles: Forms two touching “Vs” or looks like a bowtie ∠ 1 & ∠ 4 are Vertical Angles ∠ 2 & ∠ 3 are Vertical Angles ∠ 5 & ∠ 8 are Vertical Angles ∠ 6 & ∠ 7 are Vertical Angles

  18. 1 2 3 4 5 6 7 8 Special Angle Relationships Vertical Angles: Forms two touching “Vs” or looks like a bowtie ∠ 1 & ∠ 4 are Vertical Angles ∠ 2 & ∠ 3 are Vertical Angles ∠ 5 & ∠ 8 are Vertical Angles ∠ 6 & ∠ 7 are Vertical Angles

  19. 1 2 3 4 5 6 7 8 Special Angle Relationships Supplementary Angles: Add up to 180 degrees – form a straight line Examples: ∠ 1 & ∠ 2 are Supplementary Angles • ∠ 1 & ∠ 3 are Supplementary Angles • ∠ 7 & ∠ 8 are Supplementary Angles • ∠ 7 & ∠ 5 are Supplementary Angles

  20. Parallel Lines & TransversalsDAY #2

  21. 1 2 3 4 6 5 7 8 If the lines are not parallel, these angle relationships DO NOT EXIST. Special Angle RelationshipsWHEN THE LINES ARE PARALLEL ♥Alternate Interior Angles are CONGRUENT ♥Alternate Exterior Angles are CONGRUENT

  22. 1 2 3 4 6 5 7 8 If the lines are not parallel, these angle relationships DO NOT EXIST. Special Angle RelationshipsWHEN THE LINES ARE PARALLEL ♥Same Side Interior Angles are SUPPLEMENTARY ♥Same Side Exterior Angles are SUPPLEMENTARY ♥Supplementary Angles are SUPPLEMENTARY

  23. 1 2 3 4 6 5 7 8 If the lines are not parallel, these angle relationships DO NOT EXIST. Special Angle RelationshipsWHEN THE LINES ARE PARALLEL ♥Corresponding Angles are CONGRUENT ♥Vertical Angles are CONGRUENT

  24. 1 2 3 4 6 5 7 8 Let’s Practice m<1=120° Find all the remaining angle measures. 120° 60° 120° 60° 120° 60° 120° 60°

  25. Another practice problem Find all the missing angle measures. 137°

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