3 1 Parallel Lines Transversals and Angle Relationships

3. 1 Parallel Lines, Transversals and Angle Relationships Obj: 1. ) to ID relationships of 2 planes and 2 lines 2. ) to name angles formed by 2 lines and transversals

Definition Skew lines - 2 lines are skew if they do NOT intersect and are NOT in the same plane Draw and label this box in your notes. Label all segments skew to AB B D A CE, DF, FG, EH C E H G F

Definitions Continued Parallel lines-2 Lines that are in the same plane that never intersect. Transversal-Line that intersects 2 lines at different points. It’s the line in both angles when describing angle relationships.

Exterior angles t Outside the 2 lines l 1 2 4 3 5 m transversal 6 8 7

Interior Angles t Inside the 2 lines l 1 2 4 3 5 m transversal 6 8 7

*Consecutive-interior Angles…aka co-interior Angles t Angles inside the 2 lines on the same side of the transversal l 1 2 4 3 5 m transversal 6 8 7

*Alternate Interior Angles on the inside of the 2 lines and on opposite sides of the transversal t l 1 2 4 3 5 m transversal 6 8 7

*Corresponding Angles t Angles in the same spot. Both above the lines on the same side of the transversal or below lines on same side of the transversal l 1 2 4 3 5 m transversal 6 8 7

*Alternate Exterior Angles t Outside the 2 lines on opposite sides of the transversal l 1 2 4 3 5 m transversal 6 8 7

Angle Relationship Definitions Exterior anglesoutside 2 lines Angles 1, 2, 7, 8 Interior anglesinside the 2 lines Angles 3, 4, 5, 6 Co-interior angles- same side of transversal inside the 2 lines Angles 4 & 5, 3 & 6 Alternate interior angle- opposite sides of transversal inside the 2 lines Angles 3 & 5, 4 & 6 Alternate exterior angleopposite sides of transversal, outside the lines Angles 2 & 8, 1 & 7

Angle Relationship Definitions Continued Corresponding anglessame side of transversal in same position Angles 1 & 5, 4 & 8, 2 & 6, 3 & 7

Example: t ID each pair of angles Angles 6 & 10 Co-int < s Angles 9 & 11 A. I. A Angles 1 & 5 Corr. < s l 1 8 10 2 Angles 3 & 8 A. E. A Angles 7 & 12 A. I. A Angles 4 & 8 Corr. < s 5 11 7 12 6 3 9 m 4

Your Turn: ID transversal to l & m Line t or t ID the relationship between the following angles. l 1 9 t 3 2 m 7 & 12 8 & 10 2 & 12 Corr < s A. I. A A. E. A 7 8 6 11 4 5 10 12

What’s the angle relationship of angles 1 and 2? 1 The. What linesdo arethe arrows parallelmean? 2 Corresponding: Notice they are in the same position so they are congruent.

What’s the angle relationship of angles 1 and 2? 1 2 Alternate Exterior Angles: Notice they are vertical so they are congruent.

What’s the angle relationship of angles 1 and 2? 1 2 Alternate Interior Angles: Notice they are vertical so they are congruent.

What’s the angle relationship of angles 1 and 2? 1 2 Consecutive Interior Angles: Notice they supplementary. Watch

So if lines are parallel, we know? If 2 ll lines are cut by a transversal, then each pair of corresponding angles is congruent (postulate that can be used in all proofs) If 2 ll lines are cut by a transversal, then each pair of alternate interior angles is congruent If 2 ll lines are cut by a transversal, then each pair of consecutive interior angles is supplementary If 2 ll lines are cut by a transversal, then each pair of alternate exterior angles are congruent

Perpendicular Transversal Theorem In a plane, if a line is perpendicular to 1 of 2 ll lines, then it is perpendicular to the other.

Example: l Given p ll q, l is transversal of p and q 1 5 Prove: 7 Statement 1. ) p II q 3 6 2 4 8 Justification 1. ) given 2. ) Corr < s 3. ) vert. < s 4. ) Substitution p q

Example: In the figure, l II m and c ll d. Find the values of x, y, and z. l m 14 z = 98 (AIA) z=7 98 + 2 x + 5 = 180 (co-int) 98 o x = 38. 5 3 y + 8 = 98 (AEA) y = 30 c 14 zo (2 x + 5)o d (3 y + 8)o

Homework: Put this in your agenda pg 150 18 – 27 Pg 157 9 – 20, 23, 27 – 32