1. Angles and Parallel Lines Lesson 2-4 Lesson 2-4: 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 interior angles Alternative exterior angles Alternative interior angles Corresponding angles t m n Lesson 2-4: Angles and Parallel Lines

3. Vertical Angles & Linear Pair Two angles that are opposite angles. Vertical angles are congruent. Vertical Angles: Linear Pair: 1  4, 2  3, 5  8, 6  7 Supplementary angles that form a line (sum = 180) 1 & 2 ,2 & 4 , 4 &3, 3 & 1, 5 & 6,6 & 8, 8 & 7, 7 & 5 1 2 3 4 5 6 7 8 Lesson 2-4: Angles and Parallel Lines

4. 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 Continued….. Lesson 2-4: Angles and Parallel Lines

5. 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 Lesson 2-4: Angles and Parallel Lines

6. Consecutive Angles Consecutive Interior Angles: Two angles that lie between parallel lines on the same sides of the transversal. Consecutive Exterior Angles: Two angles that lie outside parallel lines on the same sides of the transversal. m3 +m5 = 180º, m4 +m6 = 180º 1 2 m1 +m7 = 180º, m2 +m8 = 180º 3 4 5 6 7 8 Lesson 2-4: Angles and Parallel Lines

7. Alternate Angles • Alternate Interior Angles: Two angles that lie between parallel lines on opposite sides of the transversal (but not a linear pair). • Alternate Exterior Angles: Two angles that lie outside parallel lines on opposite sides of the transversal. 3  6,4  5 2  7,1  8 1 2 3 4 5 6 7 8 Lesson 2-4: Angles and Parallel Lines

8. B A 1 2 10 9 12 11 4 3 C D 5 6 13 14 15 16 7 8 s t Example:If line AB is parallel to line CD and s is parallel to t, find the measure of all the angles when m< 1 = 100°. Justify your answers. m<2=80° m<3=100° m<4=80° m<5=100° m<6=80° m<7=100° m<8=80° m<9=100° m<10=80° m<11=100° m<12=80° m<13=100° m<14=80° m<15=100° m<16=80° Lesson 2-4: Angles and Parallel Lines

9. B A 1 2 10 9 12 11 4 3 C D 5 6 13 14 15 16 7 8 s t Example: If line AB is parallel to line CD and s is parallel to t, find: 1. the value of x, if m<3 = 4x + 6 and the m<11 = 126. 2. the value of x, if m<1 = 100 and m<8 = 2x + 10. 3. the value of y, if m<11 = 3y – 5 and m<16 = 2y + 20. ANSWERS: 1. 30 2. 35 3. 33 Lesson 2-4: Angles and Parallel Lines