Parallel and Perpen icular Lines. Worksheets

n Parallel and Perpen icular Lines Worksheets

Exercises 1 5 1. 2. a c b 60 a b 40 c 3. 4. a 51 52 b c d 60 b c a d 65 h i e f g 55 5. a b 163 c 70 d e Discovering Geometry Teaching and Worksheet Masters LESSON 2.5 Transparency 31 2003 Key Curriculum Press Page 1

Lesson 3.1 Angle Relationships Name Period Date For Exercises 1 8, find each lettered angle measure without using aprotractor. 1. 2. 3. 4. 112 a b c 15 a 38 40 d a 70 c b 66 42 a b 5. e 6. 7. 8. 132 d a c b b a b 100 c 70 a 110 d e c 138 For Exercises 9 14, tell whether each statement is always (A), sometimes (S), or never (N) true. 9. The sum of the measures of two acute angles equals the measure of an obtuse angle. 10. If XAY and PAQ are vertical angles, then either X, A, and P or X, A, and Q are collinear. 11. The sum of the measures of two obtuse angles equals the measure of an obtuse angle. 12. The difference between the measures of the supplement and the complement of an angle is 90. 13. If two angles form a linear pair, then they are complementary. 14. If a statement is true, then its converse is true. For Exercises 15 19, fill in each blank to make a true statement. 15. If one angle of a linear pair is obtuse, then the other is. 16. If A B and the supplement of B has measure 22, then ma. 17. If P is a right angle and P and Q form a linear pair, then mq is. 18. If S and T are complementary and T and U are supplementary, then U is a(n) angle. 19. Switching the if and then parts of a statement changes the statement to its. 25 a b Discovering Geometry Practice Your Skills CHAPTER 2 13 2003 Key Curriculum Press Page 2

Constructing Parallel Lines Name Period Date 1. Draw a line and a point not on the line. Use a compass and straightedge to construct a line through the given point parallel to the given line. 2. Repeat Exercise 1 but draw the line and point on patty paper and fold to construct the parallel line. 3. Use a compass and straightedge to construct a parallelogram. 4. Use patty paper and a straightedge to construct an isosceles trapezoid. 5. Construct a rhombus with sides equal in length to AB and having an angle congruent to P. A B P 6. Construct trapezoid ZOID with ZO and ID as nonparallel sides and AB as the distance between the parallel sides. Z O I D A B In Exercises 7 15, use the figure to determine whether each statement is true, false, or cannot be determined. 5 7 6 A B C D 1 2 3 4 7. AB BC 8. AB CD 9. 6 CD 10. The distance between 2 and 3 is 7. 11. BD AC 12. AB 5 13. CD 5 14. The distance between 1 and 4 is at least 18. 15. The distance between 1 and 4 is at most 18. Discovering Geometry Practice Your Skills CHAPTER 3 19 2003 Key Curriculum Press Page 3

Name Date 1. Construct a line parallel to the one below that passes through the point P 2. (a) Construct a line parallel to AB through Q, and another line parallel to CD also through Q (b) What is the name of the resulting 4-sided shape? Page 4

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Lesson 3.2 Special Angles on Parallel Lines Name Period Date For Exercises 1 11, use the figure at right. For Exercises 1 5, find an example of each term. 1. Corresponding angles 2. Alternate interior angles 3. Alternate exterior angles 4. Vertical angles 5. Linear pair of angles For Exercises 6 11, tell whether each statement is always (A), sometimes (S), or never (N) true. 6. 1 3 7. 3 8 8. 2 and 6 are supplementary. 9. 7 and 8 are supplementary. 10. m1 m6 11. m5 m4 For Exercises 12 14, use your conjectures to find each angle measure. 12. 13. 14. 1 2 5 6 3 4 7 8 c a b 54 65 d c b a b 54 a For Exercises 15 17, use your conjectures to determine whether or not 1 2, and explain why. If not enough information is given, write cannot be determined. 15. 16. 17. 118 1 1 48 1 62 2 95 25 2 48 2 18. Find each angle measure. 44 78 f e 64 a b d c 14 CHAPTER 2 Discovering Geometry Practice Your Skills Page 7 2003 Key Curriculum Press

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Exercise 7 p n 79 c d a 64 b 75 m q s k j i g h e 108 f 169 t 61 32 LESSON 2.6 Transparency Discovering Geometry Teaching and Worksheet Masters Page 9 2003 Key Curriculum Press

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Parallel Lines and Transversals Worksheet Name State the transversal that forms each pair of angles. Then identify the special name for the angle pair. 1 2 1. 14 and 10 3 4 5 6 7 2. 2 and 10 8 l 3. 4 and 9 4. 6 and 3 9 10 11 12 13 14 15 16 m 5. 1 and 12 6. 7 and 13 r p The three-dimensional figure shown at the right is called a right pentagonal prism. 7. Identify all segments joining points marked in plane JIH that appear to be skew to AB. 8. Which segments seem parallel to BF? 9. Which segments seem parallel to GH? 10. Identify all planes that appear parallel to plane FGH. A E B D C I J F H G Page 11

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Worksheet 3,1-3,3 Name Ill #1-4, lpefep fo the figure at the Pigh!"l 1) Name two pairs of parallel segments,, and M --7 2) Name two segments skew to NM, 3) Namÿ two transversals for parallel lines N'-O and P'-Q, andÿ and and N Q O 4) Name a' segment that is parallel to plane MRQ, :In # 5-8, Identify the special name for each pair of angles in the figure, 5) z2 and _/6 6) --/4 and/8 4 3ÿ 7) Z4 and -/5 8) Z2 and _/5 In #9-15, use the figure at the right where p//q, mzl = 78, and mz2 = 47. Find the measure of each angle, 9) mz8 = 11) mz5 = 13) mz7 : 10) m,/4 =ÿ 12) ml6 = ÿ / 14) mz8 =ÿ!5) rnz -ÿ In #16-18, find the values of x and y in each figure. 16) rnzz : GK-l L3- d+8 X: y: Page 15

17 >L X" Zn #19 & 20, flnd the values of x, y and z In each flÿre, 19) o/ib; mlln m n zo) L oqz + 18 X- Vÿw yÿ Z= Z.ÿ 21) If Zl ÿ_ Z2, which lines must be poralleip If zÿ ÿ z4, which lines must bg ÿrallel?_ 22. Given the following information, can you conclude m///7, p//q or neither., 2, 4. 5, Z3ÿ/lO ZI ÿ/13 Z4=LII ZI2ÿZI3 Z3 = /14 1 3 /77!ÿ 910 4 11 12 p Page 16

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Name: Date: Parallel and Perpendicular Lines Practice 1. Write the following using mathematical symbols. a. line AB is parallel to ray CD. b. line segment AB is perpendicular to line CD. c. ray AB is parallel to ray CD. 2. Fill in the blank with the correct vocabulary word. a. The product of two perpendicular slopes is. b. Parallel lines have slopes. c. 11/ 13 and -13/11 are called. d. lines always form a 90 degree measure. e. Horizontal lines have a slope. 3. Graph y = 3x -1 and y = 3x + 1 and tell whether they are parallel, perpendicular, or coinciding lines. How do you know? 4. Graph the following lines and state the slopes. a. y = 5x 4 b. y = -5x + 3 c. What is the product of the two slopes? Page 23

d. Are the lines perpendicular? 5. Graph the following lines and state the slopes. a. y = 4x + 5 b. y = - 1/ 4x 5 c. What is the product of the two slopes? d. Are the lines perpendicular? 6. Turn the following standard form equation into slope-intercept form and then graph. Then graph the line perpendicular to it going through the point (4, 1). 2x 3y = 9 7. Turn the following standard form equation into slope-intercept form and then graph. Then graph the line parallel to it going through the point (-3, 2). 3 x + y = 4 Page 24

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Proof Practice WS Perÿ Name Date In #1 & 2, write the algebraic proofs on your own. 1) Given: 2 (x - 3) = 26 Prove: x = 16 t e 3ÿ d 4ÿ. 2) Given: 4x - 3 = x - 12 Prove: x = -3 5fafements Reoson$ 1, 1. 2, 2, 3, 3, 4. 4. Page 27

Proof Practice WS Per Name. Date 3) state the theo.rem or postulate that makes each statÿlsmfalse' write no ÿ, Given" line roll line n EX: _/3 ÿ/.6 //lines ÿ corr z's =_ " J ÿ-- : ÿ.n t a) z2 ÿ z5 e) zl _-- z6 b)/1 _= L2 f) Z4 _= Z6 c) z2 supp Z6 g) Z4 supp zl d) -/4 supp L6 In #4-8, fill in thÿ missing,statements & reasons in the proofs, 4) Givenÿ RT = 5U Proveÿ R5 = TU Statements Rea.sgns 1. i, 2. RT= SU = 2. Segment Addition Postulate: 3. 3, 4, 4. 5) Given: ABIIdD /I _=/'2 Prove; ADII BC nts 1. ABllCb 2./B ÿ zl 3, zl ÿ/2 Reasons 1, 2, 3, C 4. 4, 5, 5, Page 28

Proef Practice WS Perÿ Name Date 6) Given: j II k k II t Proveÿ Zl ÿ Z3 Sfofeÿnfs I. k 2. Zl ÿ L5 3, 4. 7) Givenÿ RVIIT5 Zl ÿ zÿ2 Prowÿ R5 II TV Staterlÿents!, 2, 3, L4 ÿ z:3 2, Vertical z:'s are 3. 4, 6, /1=/2 4, 5, 6, 6, 7, 7, 8) Given: C II m z:l -- z3 Proveÿ j II k Statelÿentÿ i, j k 2,, 2,//lines ÿ corr Z's 3ÿ, 4ÿ Page 29 2

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Nÿme MÿL Geometry Date Period Review Sheet #1 - Chapter 3 In #1-3, fill in the missing statements or reasons for each proof. 1) ÿ=iven: a//b, c//d Prove: Z8 ÿ Z4 1 2 4 Statements 1. in 12 ÿb 2.,'8 =/'2,,,,, 2) Given: a//b; L1 ÿ/3 Prove: n//k Statements 1. 2.!3ÿZ4,, 3. Transitive,, 3) Given: x//y; Z9 ÿ Z1 Statements 1. xlly Prove: m/9 + m/6 = 180 X 2./4 &/'6 are supplementary, 3 I m ÿlÿ + m ÿ : 180, 4.,'9 ÿ,'1, 5.21_--_2 5. Vertical Zs are 6.-/ s--!, 7. me = me,.. Page 31 II

Iÿ #4-9, find the slope of each line. 4) (10,1) & (4,6) 5) (4,1) & (4,-3) 6) horizontal line 7) vertical line 8) A line parallel to the line through (2,1) and (-5,3) 9) A line perpendicular to the line through (0,2) and (4,-3) In #10-13, graph each line. 1 10) through (1, -2); slope = -- 2 11) slope = O; through (-4, 3) i i v i i i J 12) through (2, 5); perpendicular to the line through (-1,3) and (0,0) 13) slope = undefined; through (5,3) Page 32

Iÿ#14-16, determine if AB and EF are parallel, perpendicular or neither. 14) A (2,3) B(4,6) E (0,4) F (3,6) 15) A (-6,1) B (2,8) E(1,1) r (9,8) 16)A(-3,-4) B(7,-10) E(3,-1) F(6,4) Page 33 q

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Name MDL Geometry Date Period Review Sheet #2 - Chapter 3 1) Name a pair of each of the following from the figure at the right: B F parallel lines skew lines perpendicular lines A C R S 2) Name a pair of each of the following from the figure at the right: X parallel lines skew lines perpendicular lines V Y In #3-9, a//b and s//t, name each pair of angles or write none if there is no name for that pair. a4" L 3)/3 & L5 ÿ...=.. i/2 ^ f 4) L4 &/9 3F 12 ÿ4ÿ"""1"1"ÿ$ 5) z4 & z6 6)/3 &/4 7/8 171n ÿt!! 7) -'9 & z12 8) L2 & L7 9)/6 & L8 In #10-15, answer the following given that n//m and p//q. 10) If m/4 = 65, then roll2 = 11) If roll6 = 101, then ml6 = ÿm. 12) If ml3 = 85, then m/2 = ÿ. 13) If m/7 = 95, then m/14 =. 14) If roll1 = 140, then ml2 = ÿ. 15) If m/13 = 100, then roll4 =. P n Page 35

i I_ In #16-18, find the value of x so that r//s. 16) x = ÿ 17) x = t +7 t 18) x = r 2x+ÿ 19) Given a//b, mz4 = 30, ml5 = 40. Find the following, r!ll = ÿ ml7 = ml2 = ml8 = ml3 = ml9 = ml6 = 20) Given that a//b and c//d, answer the following. If ml2 = 80, then roll = ÿ. C / ÿo 1 If mz8 = 60, then ml3 = ÿ. 4 " If ml2 = 80, then ml6 =. If roll = 100, then ml9 = If mÿl = 110, then roll3 = If roll0 = 65, then roll4 =. In #21-25, tell which pair of lines are parallel given the following information. 21) L3 ÿ L15 24) Z8 -/10 22) Lll - Z14 23) L7 ÿ L1 25) L3 is supplementary to L8 P k Page 36

Name Date Period Glencoe Geometry Spiral Review WS #4 AIqebra Spiral Review: In #1-6, for each set of points, find the slope and then write the equation of the line parallel to the given line, and the line perpendicular through the point A. Both lines should be written in Slope Intercept form. 1) A(1,3) and B(3,7) 2) A(0,9) and B(9,0) 3) A(-4,-3) and B(-5,-5) Slope: Slope: Slope: Line Parallel: Line Parallel: Line Parallel: Line Perpendicular to A: Line Perpendicular to A: Line Perpendicular to A: 4) A(-2,-4) and B(1,2) 5) A(-12,9) and B(-3,3) 6) A(-4,-8) and B(1,2) Slope: Point-Slope form: Slope: Point-Slope form: Slope: Point-Slope form: Slope-Intercept form: Slope-Intercept form: Slope-Intercept form: In #7-10, evaluate the given expression: 31 2 ÿ 1 7) 4-3 8) (4-ÿ-) 1 1 1 2 7 2 3 9) 2 3 4 10) (5+1-])+(-3--4) Page 37 9

Gelometry Spiral Review: For Questions 11-13, the endpoints of two segments are given. Find each segment length. Then tell whether the segments are congruent. Ii) AB :A(6,-2), B(3,-2) FG : F(5, 2), G(1, 5) 12) CD: C(5, 4), D(0,4) LM: L(-4,-3), M(-1,1) 13) AB : A(6,-2),B(8,-2) FG : F(2, 5), G(5,1) 14) Find the value of X in the image to the right. supplement. Then state the value of its compliment and - [ 15) Circle all Z1 & z6 angle relations that apply: adjacent complementary supplementary vertical linear pairs no relationship Z3 & Z6 adjacent supplementary complementary vertical linear pairs ÿ 3ÿ,ÿ4ÿ s6j no relationship 4 Z5 & Z6 adjacent supplementary complementary vertical linear pairs Aÿ,,ÿB no relationship Z2 & Z6 adjacent supplementary complementary vertical linear pairs no relationship Page 38