Date: 5.6 Notes: Proving Lines Parallel   Lesson Objective: Recognize angle pairs that occur with parallel lines. Prove that 2 lines are parallel. CCSS: G.CO.9, 12 Prove theorems about lines and angles. Make formal geometric constructions.

Lesson 1: Identify Parallel Lines Draw a line segment x on one of your blue lines. Draw line segment y at a 40° angle on the left portion of the segment. Draw line segment z at a 40° angle to the right of y. x

Lesson 1: Identify Parallel Lines Draw a line segment x on one of your blue lines. Draw line segment y at a 40° angle on the left portion of the segment. Draw line segment z at a 40° angle to the right of y. y z 1 2 40° 3 4 40° x 5 6 7 8

Lesson 1: Identify Parallel Lines What did you construct with line segments y and z? _______________________ How do we know they are ________________? Put the appropriate marks on lines y and z in red. y z 1 2 40° 3 4 40° x 5 6 7 8

CONVERSE of Corresponding Angles Postulate: If 2 lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel. y| |z because: / 2 / 4 The other corresponding / s are: y z 1 2 40° 3 4 40° x 5 6 7 8

x and y can also be proved to be parallel by: Alternate Interior Angles CONVERSE: Examples: / 2 / __, / 3 / __ Consecutive Interior Angles CONVERSE: Examples: m/ 2 + m/ __ = 180° m/ __+ m/ __ = 180° Alternate Exterior Angles CONVERSE: Examples: / 1 / __, / __ / __

Perpendicular Transversal Converse: If 2 lines are _|_ to the same line, then they are | |.

Lesson 2: Identify Parallel Lines Given the following information, determine which lines, if any, are parallel. State the pos-tulate or theorem that justifies your answer. a. / 2 / 8 b. / 3 / 11 c. / 12 / 14 d. / 1 / 15 e. m/ 8 + m/ 13 = 180° f. / 8 / 6

Lesson 2: Identify Parallel Lines Given the following information, determine which lines, if any, are parallel. State the pos-tulate or theorem that justifies your answer. a. / 2 / 8 a| |b; Conv Alt Int / s b. / 3 / 11 c. / 12 / 14 d. / 1 / 15 e. m/ 8+m/ 13 = 180° f. / 8 / 6

Lesson 2: Identify Parallel Lines Given the following information, determine which lines, if any, are parallel. State the pos-tulate or theorem that justifies your answer. a. / 2 / 8 a| |b; Conv Alt Int / s b. / 3 / 11 l| |m; Conv. Corr. / s c. / 12 / 14 d. / 1 / 15 e. m/ 8+m/ 13 = 180° f. / 8 / 6

Lesson 2: Identify Parallel Lines Given the following information, determine which lines, if any, are parallel. State the pos-tulate or theorem that justifies your answer. a. / 2 / 8 a| |b; Conv Alt Int / s b. / 3 / 11 l| |m; Conv. Corr. / s c. / 12 / 14 a| |b; Conv Alt Ext / s d. / 1 / 15 e. m/ 8+m/ 13 = 180° f. / 8 / 6

Lesson 2: Identify Parallel Lines Given the following information, determine which lines, if any, are parallel. State the pos-tulate or theorem that justifies your answer. a. / 2 / 8 a| |b; Conv Alt Int / s b. / 3 / 11 l| |m; Conv. Corr. / s c. / 12 / 14 a| |b; Conv Alt Ext / s d. / 1 / 15 Not possible e. m/ 8+m/ 13 = 180° f. / 8 / 6

Lesson 2: Identify Parallel Lines Given the following information, determine which lines, if any, are parallel. State the pos-tulate or theorem that justifies your answer. a. / 2 / 8 a| |b; Conv Alt Int / s b. / 3 / 11 l| |m; Conv. Corr. / s c. / 12 / 14 a| |b; Conv Alt Ext / s d. / 1 / 15 Not possible e. m/ 8+m/ 13 = 180° l| |m; Conv Consec Int / s f. / 8 / 6

Lesson 2: Identify Parallel Lines Given the following information, determine which lines, if any, are parallel. State the pos-tulate or theorem that justifies your answer. a. / 2 / 8 a| |b; Conv Alt Int / s b. / 3 / 11 l| |m; Conv. Corr. / s c. / 12 / 14 a| |b; Conv Alt Ext / s d. / 1 / 15 Not possible e. m/ 8+m/ 13 = 180° l| |m; Conv Consec Int / s f. / 8 / 6

Lesson 3: Proving | | Lines Find x so that l| |m in the following situa-tions. Name the postulate or theorem. a. m/ 1 = (7x – 2)° m/ 2 = (10 – 3x)° b. m/ 1 = (4x – 23)° m/ 3 = (2x + 17)°

Lesson 4:

5.6: Do I Get It? Yes or No Given the following information, determine which lines, if any, are parallel. State the pos-tulate or theorem that justifies your answer. / 1 / 6 / 2 / 3 / 3 / 5 m/ 4 + m/ 5 = 180

5.6: Do I Get It? Continued 5. Find m/ MRQ so that a| |b. Show your work. Name the postulate or theorem that justifies your answer. Find m/ LRP.