2 1 3 4 Angles and Parallel Lines

2 1 3 4 Angles and Parallel Lines 6 5 7 8

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 are formed m t Exterior angles: Outside the lines Interior angles : Between the lines n 2

Vertical Angles & Linear Pair Vertical Angles: Two angles that are opposite angles. Vertical angles are congruent. 1 4, 2 3, 5 8, 6 7 Linear Pair: Supplementary angles that form a straight line (sum = 180 ) 1 & 2 , 2 & 4 , 4 & 3, 3 & 1, 5 & 6, 6 & 8, 8 & 7, 7 & 5 1 3 5 7 2 4 6 8 3

Corresponding Angles: Two angles, on the same side of the transversal, that occupy corresponding positions, one interior and one exterior. 2 and 6, 1 and 5, 3 and 7, 4 and 8 1 3 5 7 2 4 6 8 4

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

Consecutive Angles Consecutive Interior Angles: Two angles that lie between the lines, both on the same side of the transversal. 3 and 5 , 4 and 6 Consecutive Exterior Angles: Two angles that lie outside the lines, both on the same side of the transversal. 1 and 7 , 2 and 8 1 3 5 7 2 4 6 8 6

Example List all pairs that fit the description a. Corresponding < 4 and < 2 < 3 and < 1 < 5 and < 7 b. Alternate Exterior < 4 and < 8 < 1 and < 5 c. Alternate Interior < 2 and < 6 < 3 and < 7 d. Consecutive Interior < 3 and < 2 < 6 and < 7 < 6 and < 8

Example Complete the statement with corresponding, alternate exterior, alternate interior, or consecutive interior. 1. < 4 and < 8 are Alternate interior 2. < 2 and < 6 are Alternate exterior 3. < 1 and < 8 are Consecutive interior 4. < 7 and < 2 are Consecutive exterior 5. < 4 and < 6 are Corresponding 6. < 5 and < 7 are Vertical

Investigation Let’s check out the relationship of these angle pairs!

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 10

Example Given a ll b, find each measure given that m < 6 = 67°.

Example State the postulate or theorem that justifies the statement.

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. A 1 4 C 5 8 m<2=80° m<3=100° m<4=80° s 2 9 12 3 6 10 11 B D 13 14 16 15 7 t 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° 13

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