The objective of this lesson is: Understand the Transversal To identify alternate angles and corresponding angles. To calculate angles between parallel lines giving a reason for the answers Determine interior and exterior angles
Transversal Definition: A line that intersects two or more lines in a plane at different points is called a transversal. 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
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 Consecutive exterior angles
Alternate Angles Alternate Interior Angles: Two angles that lie between parallel lines on opposite sides of the transversal (but not a linear pair). 3 6, 4 5 Alternate Exterior Angles: Two angles that lie outside parallel lines on opposite sides of the transversal. 2 7, 1 8 1 2 3 4 5 6 7 8
Alternate angles You need a pair of parallel lines. Alternate angles Draw any line to cut the pair of parallel lines. What angle is the same as the blue one?
How do you tell angles are alternate? Look for a letter Z in any orientation.
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
Corresponding angles You need a pair of parallel lines. corresponding Draw any line to cut the pair of parallel lines. What angle is the same as the red one?
How do you tell angles are corresponding? Look for a letter F in any orientation.
Examples Find the values of the letters, give reasons. a = 76 : Angles on a straight line add up to 180 b = 76 : Corresponding angles c = 104 : Angles on a straight line add up to 180 d = 104 : Alternate angles
Examples Find the values of the letters, give reasons. 68 a = 68 : Corresponding angles b = 32 : Corresponding angles c = 80 : Angles in a triangle add up to 180
Summary You should be able to identify alternate angles and corresponding angles. You should be able to calculate angles between parallel lines giving a reason for the answers