Parallel lines and Transversals Sec 3.1 Sol:G.3a
Lesson 2-3: Pairs of Lines Parallel Lines Parallel lines are coplanar lines that do not intersect. Arrows are used to indicate lines are parallel. The symbol used for parallel lines is ||. In the above figure, the arrows show that line AB is parallel to line CD. With symbols we denote, . Lesson 2-3: Pairs of Lines
Lesson 2-3: Pairs of Lines OBLIQUE LINES Oblique lines are lines that intersect, but do NOT form a right angle. m n Lesson 2-3: Pairs of Lines
Skew Lines and Parallel Planes Definition: Skew lines are lines that are non-coplaner and do not intersect. Ex: What lines are skew to ? Definition: Parallel planes are planes that do not intersect. Ex : Name a set of parallel planes.
Example
Lesson 2-4: Angles and Parallel Lines Transversal Definition: A line that intersects two or more lines in a plane at different points is called a transversal. Note: Transversals intersects do not always have to be Parallel. When a transversal t intersects line n and m, eight angles of the following types are formed: Exterior angles Interior angles Consecutive interior angles Alternative exterior angles Alternative interior angles Corresponding angles t m n Lesson 2-4: Angles and Parallel Lines
Exterior and Interior Angles Exterior Angles: Angles that are on the “outside” of the two “clusters” Interior Angles: Angles that are in the “middle “ of the two “clusters”
Consecutive Interior Angles Consecutive Interior Angles: (Same-side Interior Angles) Are on the same side of the transversal. On the inside.
Alternate Exterior and Alternate Interior Angles Alternate Exterior Angles: Are on the opposite sides (or they alternate sides) of the transversal. Are on the outside. Alternate Interior Angles: Are on the opposite sides of the transversal. Are on the inside.
Corresponding Angles Corresponding Angles: Occupy the same place in the different clusters.
m t 1 8 l 5 10 2 4 11 7 12 6 9 3 Identify each pair of angles as Alt. interior, Alt. exterior, Corresponding or Consecutive interior angles. a. b. c. d. e. f. Identify all pairs of vertical angles. Identify all linear pairs.
Assignment CW: 59-60 1-12, 14, 16-23,27 Hw: pg 144-145 11-29, 37-42
Angles and Parallel Lines Section 3.2 Sol: G.3a, c, f E.Q.: Compare and contrast parallel lines with a transversal and non-parallel lines and a transversal.
Angles and Parallel Lines If two parallel lines are cut by a transversal, then the following pairs of angles are congruent. Corresponding angles Alternate interior angles Alternate exterior angles If two parallel lines are cut by a transversal, then the following pairs of angles are supplementary. Consecutive interior angles Continued….. Lesson 2-4: Angles and Parallel Lines
3-1 Corresponding angles postulate If two parallel lines are cut by a transversal, then each pair of corresponding angles are congruent. 2 6, 1 5, 3 7, 4 8 1 2 3 4 5 6 7 8 Lesson 2-4: Angles and Parallel Lines
3-2 Consecutive Interior Angles Theroem If two parallel lines are cut by a transversal, then then each pair of consecutive interior angles is supplementary. m3 +m5 = 180º, m4 +m6 = 180º 1 2 3 4 5 6 7 8 Lesson 2-4: Angles and Parallel Lines
Lesson 2-4: Angles and Parallel Lines Alternate Angles 3-1 Alternate Interior Angles Thereom: If two parallel lines are cut by a transversal, then each pair of alternate interior angles are Congruent. 3-3 Alternate Exterior Angles: If two parallel lines are cut by a transversal, then each pair of alternate exterior angles are Congruent. 3 6, 4 5 2 7, 1 8 1 2 3 4 5 6 7 8 Lesson 2-4: Angles and Parallel Lines
3-4 Perpendicular Transversal Thereom In a plane, if a line is perpendicular to one or more parallel lines, then it is perpendicular to the other. l||m and a||b l m b a
Assignments CW:WB pg 63-64 1-12,14,15,16 Homework:Pg 153-154 7-9,12-20,22,23-24