Parallel lines-amp-transversals edited
- 2. A B D C Parallel Lines and Transversals What would you call two lines which do not intersect? Parallel A solid arrow placed on two lines of a diagram indicate the lines are parallel. The symbol || is used to indicate parallel lines. AB || CD Interior Exterior Exterior
- 3. Parallel Lines and Transversals A slash through the parallel symbol || indicates the lines are not parallel. AB || CD A D B C
- 4. Transversal A line, ray, or segment that intersects 2 or more COPLANAR lines, rays, or segments. Parallel lines transversal Non-Parallel lines transversal Interior Exterior Exterior Interior Exterior Exterior
- 5. Parallel Lines and Transversals Transversal - A transversal is a line which intersects two or more lines in a plane. The intersected lines do not have to be parallel. t mkj Lines j, k, and m are intersected by line t. Therefore, line t is a transversal of lines j, k, and m.
- 6. interior INTERIOR –The space INSIDE the 2 lines EXTERIOR -The space OUTSIDE the 2 lines exterior exterior
- 7. 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 1 4 2 65 7 8 3 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 Interior Exterior Exterior
- 8. Special Angle Relationships 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 1 4 2 65 7 8 3 If the lines are not parallel, these angle relationships DO NOT EXIST. Interior Exterior Exterior
- 9. Corresponding Angles & Consecutive Angles Corresponding Angles: Two angles that occupy corresponding positions. ∠ 2 ≅ ∠ 6, ∠ 1 ≅ ∠ 5, ∠ 3 ≅ ∠ 7, ∠ 4 ≅ ∠ 8 1 2 3 4 5 6 7 8 Interior Exterior Exterior
- 10. Corresponding Angles When two parallel lines are cut by a transversal, pairs of corresponding angles are formed. Four pairs of corresponding angles are formed. Corresponding pairs of angles are congruent. ∠GPB = ∠PQE ∠GPA = ∠PQD ∠BPQ = ∠EQF ∠APQ = ∠DQF Line M BA Line N D E L P Q G F Line L
- 11. Same Side Interior/Exterior Angles Same Side Interior Angles: Two angles that lie between parallel lines on the same sides of the transversal. Same Side Exterior Angles: Two angles that lie outside parallel lines on the same sides of the transversal. m∠3 +m∠5 = 180º, m∠4 +m∠6 = 180º m∠1 +m∠7 = 180º, m∠2 +m∠8 = 180º 1 2 3 4 5 6 7 8 Interior Exterior Exterior
- 12. The angles that lie in the area between the two parallel lines that are cut by a transversal, are called interior angles. A pair of interior angles lie on the same side of the transversal. The measures of interior angles in each pair add up to 1800 . InteriorAngles Line M BA Line N D E L P Q G F Line L 600 1200 1200 600 ∠BPQ + ∠EQP = 1800 ∠APQ + ∠DQP = 1800 Interior Exterior Exterior
- 13. Alternate Interior/Exterior Angles • Alternate Interior Angles: Two angles that lie between parallel lines on opposite sides of the transversal (but not a linear pair). Alternate Exterior Angles: Two angles that lie outside parallel lines on opposite sides of the transversal. ∠ 3 ≅ ∠ 6, ∠ 4 ≅ ∠ 5 ∠ 2 ≅ ∠ 7, ∠ 1 ≅ ∠ 81 2 3 4 5 6 7 8 Interior Exterior Exterior
- 14. Alternate InteriorAngles Alternate angles are formed on opposite sides of the transversal and at different intersecting points. Line M BA Line N D E L P Q G F Line L ∠BPQ = ∠DQP ∠APQ = ∠EQP Pairs of alternate angles are congruent. Two pairs of alternate angles are formed.
- 15. Let’s Practice m<1=120° Find all the remaining angle measures. 1 4 2 65 7 8 3 60° 60° 60° 60° 120° 120° 120° 120°
- 16. 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° 120° 60° 60° 40° 60° 60° 180-(40+60)= 80° 80° 80° 80° 100° 100°
- 17. Name the pairs of the following angles formed by a transversal. Line M BA Line N D E P Q G F Line L Line M BA Line N D E P Q G F Line L Line M BA Line N D E P Q G F Line L 500 1300