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. D F G A H B C E Label all segments skew to AB CE, DF, FG, EH

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

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

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

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

*Corresponding Angles 1 2 4 3 5 6 8 7 transversal l m 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

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

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

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

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

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

What’s the angle relationship of angles 1 and 2? The lines are parallel What do the arrows mean? 2 Corresponding: Notice they are in the same position so they are congruent.

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

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

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

Example: In the figure, l II m and c ll d. Find the values of x, y, and z. c d m l 14zo (2x + 5)o 98o (3y + 8)o 14z = 98 (AIA) z = 7 98 + 2x + 5 = 180 (co-int) x = 38.5 3y + 8 = 98 (AEA) y = 30

Homework: Put this in your agenda pg 150 18 – 27