1 Angles and Parallel Lines
2 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 angles Alternate angles t m n
3 Vertical Angles & Linear Pair Vertical Angles: Linear Pair: 1 4, 2 3, 5 8, 6 7 Two angles that are opposite angles. Vertical angles are congruent. 1 & 2, 2 & 4, 4 & 3, 3 & 1, 5 & 6, 6 & 8, 8 & 7, 7 & 5 Supplementary angles that form a line (sum = 180 )
4 Angles and Parallel Lines If two parallel lines are cut by a transversal, then the following pairs of angles are congruent. 1. Corresponding angles 2. Alternate interior angles 3. Alternate exterior angles If two parallel lines are cut by a transversal, then the following pairs of angles are supplementary. 1. Consecutive interior angles 2. Consecutive exterior angles Continued…..
5 Corresponding Angles Corresponding Angles: Two angles that occupy corresponding positions. Corresponding Angles Postulate: If two parallel lines are cut by a transversal, then the Corresponding angles are congruent. 2 6, 1 5, 3 7, 4
6 Same Side or Consecutive Angles Consecutive Interior Angles: Two angles that lie between parallel lines on the same sides of the transversal. Consecutive Interior Angles Theorem: If two parallel lines are cut by a transversal, then the Consecutive Interior Angles are supplementary. m 3 +m 5 = 180º, m 4 +m 6 = 180º
7 Same Side or Consecutive Angles Consecutive Exterior Angles: Two angles that lie outside parallel lines on the same sides of the transversal. Consecutive Exterior Angles Theorem: If two parallel lines are cut by a transversal, then the Consecutive Exterior Angles are supplementary. m 1 +m 7 = 180º, m 2 +m 8 = 180º
8 Alternate Angles Alternate Interior Angles: Two angles that lie between parallel lines on opposite sides of the transversal (but not a linear pair). Alternate Interior Angles Theorem: If two parallel lines are cut by a transversal, then the Alternate Interior Angles are congruent. 3 6, 4
9 Alternate Angles Alternate Exterior Angles: Two angles that lie outside parallel lines on opposite sides of the transversal. Alternate Exterior Angles Theorem: If two parallel lines are cut by a transversal, then the Alternate Exterior Angles are congruent. 2 7, 1
Example 1 Find all numbered angles Angles and Parallel Lines 10 60°
Example 2 Find x and y Angles and Parallel Lines 11 AB C D 30 5y 2x (x-y)