3-2 Angles and Parallel Lines page 180

1 2 1 2 PROPERTIES OF PARALLEL LINES POSTULATE POSTULATE 15 Corresponding Angles Postulate If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. 1 2 1 2

3 4 3 4 PROPERTIES OF PARALLEL LINES THEOREMS ABOUT PARALLEL LINES THEOREM 3.4 Alternate Interior Angles If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. 3 4 3 4

5 6 m 5 + m 6 = 180° PROPERTIES OF PARALLEL LINES THEOREMS ABOUT PARALLEL LINES THEOREM 3.5 Consecutive Interior Angles If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary. m 5 + m 6 = 180° 5 6

7 8 7 8 PROPERTIES OF PARALLEL LINES THEOREMS ABOUT PARALLEL LINES THEOREM 3.6 Alternate Exterior Angles If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. 7 8 7 8

j k PROPERTIES OF PARALLEL LINES THEOREMS ABOUT PARALLEL LINES THEOREM 3.7 Perpendicular Transversal If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other. j k

1  3 Corresponding Angles Postulate Proving the Alternate Interior Angles Theorem Prove the Alternate Interior Angles Theorem. SOLUTION GIVEN p || q PROVE 1 2 Statements Reasons p || q Given 1 1  3 Corresponding Angles Postulate 2 3 3  2 Vertical Angles Theorem 1  2 Transitive property of Congruence 4

which postulate or theorem you use. Using Properties of Parallel Lines Given that m 5 = 65°, find each measure. Tell which postulate or theorem you use. SOLUTION m 6 = m 5 = 65° Vertical Angles Theorem Linear Pair Postulate m 7 = 180° – m 5 = 115° Corresponding Angles Postulate m 8 = m 5 = 65° Alternate Exterior Angles Theorem m 9 = m 7 = 115°

parallel lines to find the value of x. PROPERTIES OF SPECIAL PAIRS OF ANGLES Using Properties of Parallel Lines Use properties of parallel lines to find the value of x. SOLUTION Corresponding Angles Postulate m 4 = 125° Linear Pair Postulate m 4 + (x + 15)° = 180° Substitute. 125° + (x + 15)° = 180° Subtract. x = 40°

Ex. 2 Find the values of x, y, and z MA //HT and NG//EL 2x = 72 X = 36 5y + 2 = 72 5y = 70 Y = 14 4z + 72 = 180 4z = 108 Z = 27 N E M A 4z 2x H T 72 5y+2 G L

Given p//q , m<1 =107, and m<11 = 48 Given p//q , m<1 =107, and m<11 = 48. Find the measure of each angle. q p 1 11

Find x and y. 4x-5 3y+1 3x+11

Find x and y. Given that a//b, find x and y. a 6y 9x+12 13y-10 b

Class work on page 183 problems 1-10 Homework on page 183 problems 11-29