Angles and Parallel Lines MCC8.G.5 Angles and Parallel Lines

Intersecting Lines Lines that cross at exactly one point.

Perpendicular Lines Lines that intersect to form right angles.

PARALLEL LINES Def: line that do not intersect. Illustration: Notation: l || m AB || CD A B C D l m

Examples of Parallel Lines Hardwood Floor Opposite sides of windows, desks, etc. Parking slots in parking lot Parallel Parking Streets

Examples of Parallel Lines Streets: Belmont & School

Transversal Definition: A line that intersects two or more lines in a plane at different points is called a transversal. t m n

Vertical Angles & Linear Pair Two angles that are opposite angles. Vertical angles are congruent.  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

Supplementary Angles/ Linear Pair Two angles that form a line (sum=180) 1 2 3 4 5 6 7 8 t 1+2=180 2+4=180 4+3=180 3+1=180 5+6=180 6+8=180 8+7=180 7+5=180

Supplementary Angles/ Linear Pair Find the measures of the missing angles t ? 108  72  180 - 72 ? 108 

Complementary Angles Two angles whose measures add to 90˚.

Adjacent Angles Angles in the same plane that have a common vertex and a common side.

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…..

Corresponding 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

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

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

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

If line AB is parallel to line CD and s is parallel to t, find: Example: 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. t 16 15 14 13 12 11 10 9 8 7 6 5 3 4 2 1 s D C B A ANSWERS: 1. 30 2. 35 3. 33