October 16, proving lines parallel ink.notebook. page Prove Lines Parallel. page 113. Standards. page 115.
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1 3.5 proving lines parallel ink.notebook page 113 page Prove Lines Parallel Lesson Objectives page 115 Standards Lesson Notes page Proving Lines Parallel Press the tabs to view details. 1
2 Lesson Objectives Standards Lesson Notes After this lesson, you should be able to successfully prove if lines are parallel. Lesson Objectives Standards Lesson Notes G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. G.CO.9 Prove theorems about lines and angles. G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Press the tabs to view details. Press the tabs to view details. Postulate 3.5 Parallel Postulate If given a line and a point not on the line, then there exists line through the point that is parallel to the given line. P Postulate 3.4 Converse of Corresponding Angles Postulate If 2 lines are cut by a transversal so that corresponding angles are congruent, then the lines are. 2
3 3.5 proving lines parallel ink.notebook Theorem 3.4 Perpendicular Transversal Theorem In a plane, if a line is perpendicular to one of 2 parallel lines, then it is to the other. Theorem 3.5 Alternate Exterior Angles Converse If 2 lines in a plane are cut by a transversal so that a pair of alternate exterior angles is congruent, then the lines are. Theorem 3.6 Consecutive Interior Angles Converse If 2 lines in a plane are cut by a transversal so that a pair of consecutive interior angles is supplementary, then the lines are. Theorem 3.7 Alternate Interior Angles Converse If 2 lines in a plane are cut by a transversal so that a pair of alternative interior angles is congruent, then the lines are. 3
4 3.5 proving lines parallel ink.notebook Theorem 3.8 Perpendicular Transversal Converse In a plane, if two lines are perpendicular to the same line, then they are. Ways to prove 2 lines parallel Corresponding angles congruent Alt interior angles congruent Alt Exterior angles congruent Consecutive angles are supplementary Two lines are perpendicular to the same line Click me me Click me Click Click me Click me 4
5 3.5 proving lines parallel ink.notebook 1. In the figure, a Ç b and 1 is congruent to 3. Prove x Ç y. b a 2 1 y 3 2. In the figure, x Ç y and 1 is congruent to 3. Prove a Ç b. x b a x y 5
6 Find the value of x that makes a «b. Show your work. Identify the postulate a) (5x 7) a Find the value of x that makes a «b. Show your work. Identify the postulate b) (2x + 3) a 98 b 71 b Find the value of x that makes a «b. Show your work. Identify the postulate c) (5x 5) a b (6x 20) 6
7 Extra Proof a) The reasons necessary to complete the following proof are scrambled up below. To complete the proof, number the reasons to match the corresponding statements. PRACTICE 7
8 Given the following information, determine which lines, if any, are parallel. State the postulate or theorem that justifies your answer m 5 + m 12 =
9
10 Prove: «m and r «s Answers: 1. a «b, Alt Int Con Thm 3. «m, Alt Ext Con Thm 5. x = 22, Consec Int Con Thm 7. x = 6, Alt Int Con Thm 9. x = 13.83, Vert Thm, Consec Int Con Thm 11. x = 7, Alt Int Con Thm 13. Given; Angle Add Post; Given; Def of Comp; Substitution; Def of º lines; If 2 lines º to same line, then lines «10
11 In the book, do pages , problems: 8 15, 23, 44,
12 44. 12
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