Geometry. Unit 3 Parallel and Perpendicular Lines. Name:

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1 Geometry Unit 3 Parallel and Perpendicular Lines Name: 1

2 Geometry Chapter 3 Parallel and Perpendicular Lines ***In order to get full credit for your assignments they must me done on time and you must SHOW ALL WORK. *** 1. (3-1) Parallel Lines and Transversals Day 1 Page # even 2. (3-2) Angles and Parallel Lines Day 1 Page # 14 25, Wrap-Up (3-1) and (3-2) 3-1/3-2 Practice Worksheet and 3-2 Application WS 4. (3-3) Slopes of Lines Day 1 Page 142 # even 5. (3-3) Slopes of Lines Day Practice Worksheet and 3-3 Application WS 6. (3-4) Equations of Lines Day 1 Page 148 # odd, (3-4) Equations of Lines Day Practice Worksheet and 3-4 Application WS 8. (3-5) Proving Lines Parallel Day 1 Page 155 # 13 24, 26 31, 38, (3-5) Proving Lines Parallel Day 2 Section 3-5 Practice Worksheet 10. Chapter 3 Review WS 2

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4 Date: Section 3 1: Parallel Lines and Transversals Notes Parallel Lines: coplanar lines that do not Symbol: Ex: Parallel Planes: that do not Ex: Skew Lines: lines that do not and that are not Example #1: Refer to the figure on the right. a.) Name all planes that are parallel to plane AEF. b.) Name all segments that intersect AF. c.) Name all segments that are parallel to DC. d.) Name all segments that are skew to AD. 4

5 Transversal: a line that intersects or more lines in a plane at different Ex: Example #2: Identify the pairs of lines to which each given line is a transversal. a.) p b.) r c.) q d.) t Key Concept (Transversals and Angles): Transversal p intersects lines q and r. a.) Exterior Angles b.) Interior Angles c.) Consecutive Interior Angles d.) Alternate Exterior Angles e.) Alternate Interior Angles f.) Corresponding Angles 5

CRITICAL THINKING 1.) Find the Error: Kenisha and Eric are naming alternate interior angles in the figure at the right. One of the angles must be 4. Who is correct? Explain your reasoning. 2.

6 CRITICAL THINKING 1.) Find the Error: Kenisha and Eric are naming alternate interior angles in the figure at the right. One of the angles must be 4. Who is correct? Explain your reasoning. 2.) A good way to remember new mathematical terms is to relate them to words that you use in everyday life. Many words start with the prefix trans-, which is a Latin root meaning across. List four English words that start with trans-. How can the meaning of this prefix help you remember the meaning of transversal? 6

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8 Discovering Properties of Parallel Lines Directions: 1. Using the lines on a piece of paper as a guide, draw a pair of parallel lines. 2. Draw a transversal intersecting the parallel lines and number the angles formed from 1 to Use a protractor to measure each of the numbered angles and fill in the chart below. Angle Measure Angle Measure Using the table and your picture, make as many different observations as possible. (Make sure to include all eight angles) 8

9 Using the table, your picture, and your observations, identify every pair of each of the following types of angles and make a conjecture about their measures. 1. Vertical angles: Conjecture: 2. Linear pairs: Conjecture: 3. Corresponding angles: Conjecture: 4. Alternate Interior Angles: Conjecture: 5. Alternate Exterior Angles Conjecture: 6. Consecutive Interior Angles: Conjecture: 9

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11 Date: Section 3 2: Angles and Parallel Lines Notes IF TWO PARALLEL LINES ARE CUT BY A TRANSVERSAL, THEN: By the Corresponding Angles Postulate each pair of corresponding angles is. By the Alternate Interior Angles Theorem each pair of alternate interior angles is. By the Alternate Exterior Angles Theorem each pair of alternate exterior angles is. By the Consecutive Interior Angles Theorem each pair of consecutive interior angles is. Example #1: In the figure, m and m angle. a.) 1 b.) 6. Find the measure of each c.) 2 d.) 10 e.) 13 f.) 15 11

12 Example #2: Find x and y in the following figure. Example #3: Find x and y in the following figure. Example #4: Find 1. 12

CRITICAL THINKING For questions 1 and 2, refer to the picture at the right. 1.) Determine whether 1 is always, sometimes, or never congruent to 2. Explain.

13 CRITICAL THINKING For questions 1 and 2, refer to the picture at the right. 1.) Determine whether 1 is always, sometimes, or never congruent to 2. Explain. 2.) Determine the minimum number of angle measures you would have to know to find the measures of all of the angles in the figure. Explain your reasoning. 13

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15 Date: Section 3 3: Slopes of Lines Notes Slope the ratio of a line s to its slope = Example #1: Find the slope. a.) b.) c.) d.) Example #2: For one manufacturer of camping equipment, between 1990 and 2000 annual sales increased by $7.4 million per year. In 2000, the total sales were $85.9 million. If sales increase at the same rate, what will be the total sales in

16 Example #3: Find the slope of l, m, and n. Compare the slopes of each. Two nonvertical lines have the slope if and only if they are. Two nonvertical lines are if and only if the product of their slopes is. Example #4: Determine whether and are parallel, perpendicular, or neither. a. F(1, -3), G(-2,-1), H(5,0), J(6,3) b. F(4,2), G(6, -3), H(-1, 5), J(-3, 10) 16

CRITICAL THINKING 1.) Find the Error: Curtis and Laura calculated the slope of a line containing A(15, 4) and B(-6, -13). Who is correct? Explain your reasoning. 2.

17 CRITICAL THINKING 1.) Find the Error: Curtis and Laura calculated the slope of a line containing A(15, 4) and B(-6, -13). Who is correct? Explain your reasoning. 2.) The maximum recommended slope of a wheelchair ramp is 1/12. A business is installing a wheelchair ramp that rises 22 inches over a horizontal length of 228 inches. Is the ramp steeper then recommended? Be sure to show all of your work, and explain your reasoning. 17

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19 Date: Section 3 4: Equations of Lines Notes Slope-Intercept Form Example #1: Write an equation in slope-intercept form of the line with slope of 4 and y-intercept of 1. Example #2: at (0, -8). Write an equation in slope-intercept form of the line with slope 5 and a point Example #3: at (-3, 6). Write an equation in slope-intercept form of the line with slope 2 and a point 19

20 Point-Slope Form Example #4: (-10, 8). Write an equation in point-slope form of the line whose slope is 3 5 that contains Example #5: Write an equation in slope intercept form for a line containing (4, 9) and (-2, 0). Example #6: Write an equation in slope-intercept form for a line containing (1, 7) that is 1 perpendicular to the line y x

21 CRITICAL THINKING 1.) The price of a pair of Jordan s can be represented by the linear equation P = 3.52t + 65, where t = 0 corresponds to Explain the meaning of the slope and y-intercept. Use this equation to determine how much a pair of Jordan s will cost in

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23 Date: Section 3 5: Proving Lines Parallel Notes IF TWO LINES IN A PLANE ARE CUT BY A TRANSVERSAL SO THAT: Corresponding angles are, then the lines are. A pair of alternate exterior angles is, then the two lines are. A pair of alternate interior angles is, then the lines are. A pair of consecutive interior angles is, then the lines are. Ask yourself, What if they were parallel Example #1: Determine which lines, if any, are parallel. 23

24 Example #2: Given the following information, determine which lines, if any, are parallel. State the postulate or theorem that justifies your answer. a.) 2 8 b.) 9 16 c.) 2 10 d.) 6 15 Example #3: Find x so that a b. ] Example #4: Find y so that l m. 24

25 CRITICAL THINKING 1.) Describe two situations in your own life in which you encounter parallel lines. How could you verify that the lines are parallel? 2.) When striping the practice football field, Coach Novak first painted the sidelines. Next he marked off 10-yard increments on one sideline. He then constructed lines perpendicular to the sidelines at each 10-yard mark. Why does this guarantee that the 10-yard lines will be parallel? 25

3.1 parallel lines and transversals

VOCAB Parallel lines- 3.1 parallel lines and transversals Skew lines- Parallel planes- Transversal- Interior < s Transversal Angle Pair Relationships Exterior < s Same side Interior < s (consecutive interiors