Be able to determine relationships between specific pairs of angles and use algebra to find specific angle measurements. Quick Review: Find the value of x and the measure of each angle. Justify each step! 3x3x 2x x + 2x + 50 = 180 5x + 50 = 180 5x = 130 x = 26 3(26) = 78 2(26) + 50 = 102 ||  CIA are supp simplify subtraction division

Theorem: When lines are parallel, alternate interior angles are ____! Theorem: When lines are parallel, consecutive interior angles are _________! Theorem: When lines are parallel, alternate exterior angles are _________! Theorem: When lines are parallel, consecutive exterior angles are _________!

m  1 = m  2 = m  3 = m  4 = m  5 = m  6 = m  7 = m  1 = m  2 = m  3 = m  4 = m  5 = m  6 = m  7 =

75° 3n -15 ° x 13 - x Find the value of the variables in each picture x + 13 – x = x = 180 9x = 99 x = = 3n – = 3n n = 30

m  4 = 4y + 30 m  5 = 7y + 6 Given 24 = 3y AIA Theorem Substitution 4y + 30 = 7y +6 m  4 = m  5 8 = yDivision Subtraction

L.T.: Be able to prove lines are parallel using the properties of the special angle pairs Quick Review: Find the value of x and justify each step. Find each angle measure. 3x x -25 5x – x + 45 = 180 8x + 20 = 180 x = 15/2 8x= 60 SSI Theorem Simplify Subtract Divide

Converse of Corresponding Angle Postulate: If two lines and a transversal form CORRESPONDING angles that are CONGRUENT, then the two lines are ________________! Where are there parallel lines in the pictures? 45° 37° 90° 89°

Converse of Alternating Interior Angle Theorem: If two lines and a transversal form ALTERNATING INTERIOR angles that are CONGRUENT, then the two lines are ________________! 100° Where are there parallel lines in the pictures? 50° 130° NONE

Where are there parallel lines in the pictures? 70° 110°100° 80° 75° 115° Converse of Consecutive Interior Angle Thm: If two lines and a transversal form CONSECUTIVE INTERIOR angles that are SUPPLEMENTARY, then the two lines are ________________! NONE parallel

Converse of ALTERNATE EXTERIOR Angle Thm: If two lines and a transversal form ALTERNATE EXTERIOR angles that are CONGRUENT, then the two lines are ________________! 6x - 24 x +116 Solve for x so the lines m and n are // m n parallel x = 6x = 5x x = 28

rv t  2 =  8  12 +  13 = 180  4 =  6  14 =  15  9 =  13  2 =  8  12 +  13 = 180  4 =  6  14 =  15  9 =  13 Converse of AEA Converse of CIA Converse of AIA Converse of Vertical Angles Converse of Corr

2x ° 2x x - 40° 2x = 180 2x + 50 = 180 2x = 130 x = 65 2x + 40 = 4x = 2x = 2x x = 40

Theorem: If two lines are parallel to the same line, then they are parallel to each other! Theorem: If two lines are perpendicular to the same line, then they are parallel to each other!

A D C B 1 23  2 =  3  1 =  2 Given Substitution (transitive) Converse of AIA

Are the lines parallel? Explain. 50°