1. What is the difference between complementary and supplementary angles?

Transcription

1 Name 1 Date Angles Intrductin t Angles Part 1 Independent Practice 1. What is the difference between cmplementary and supplementary angles? 2. Suppse m TOK = 49. Part A: What is the measure f the angle cmplement f TOK? Part B: What is the measure f the angle supplement f TOK? 3. Suppse m YES = 113. Part A: What is the measure f the angle cmplement f YES? Part B: What is the measure f the angle supplement f YES? 4. Angle Z is 21 degrees larger than twice the measure f angle T. If Z and T are supplementary, what is the measure f angle T? Sectin 3 Tpic 1

2 2 5. On line l, m p = 21x + 25 and m n = 675x n p l Part A: Determine the value f x. Part B: Determine the measure f p and n in degrees. 6. Cnsider the fllwing figure. C A B The measure f the supplement f ABC is (18x + 22) degrees. The measure f the cmplement f ABC is (9x 5) degrees. Determine m ABC. Sectin 3 Tpic 1

3 3 7. In the figure belw, m a = 3x + 5, m b = 5x 18, and m c = 7x 2. c b a Part A: Are a and b cmplementary? Justify yur answer. Part B: Determine m a, m b, and m c. Sectin 3 Tpic 1

4 Name 4 Date Angles Cnstructins f Angles, Perpendicular Lines, and Parallel Lines Independent Practice 1. Cpy the fllwing image and sketch the cnstructin belw. Sectin 3 Tpic 10

5 5 2. Cnstruct a cpy f A belw. A 3. Cnstruct a line thrugh R perpendicular t q. Sectin 3 Tpic 10

6 6 4. Cnstruct a line thrugh M parallel t CD. M C D 5. Cnstruct a line segment parallel t PQ and name it AB. Then, cnstruct a transversal t such that a pair f alternate interir angles is cngruent t Z shwn belw. P Q Z Sectin 3 Tpic 10

7 Name 7 Date Angles Intrductin t Angles Part 2 Independent Practice 1. What is the measure f an angle if its sides are equal rays? Prvide an example. 2. Cmplete the fllwing statement. If k is a half-plane determined by QR, then fr every real number, 0 < x 180, there is exactly ne ray, QP, that lies in k such that m PQR =. Justify the validity f this statement. 3. Use a prtractr t measure the fllwing angles and classify each angle as btuse, right, acute, straight, r reflex. P Q A M B R Sectin 3 Tpic 2

8 8 4. Use the figure belw t fill in the blanks that define angles FGK, FGH, and KGH as acute, btuse, right r straight. H F K G L FGL is a(n) angle. HGF is a(n) angle. KGH is a(n) angle. KGF is a(n) angle. KGL is a(n) angle. HGL is a(n) angle. 5. If an angle is btuse, what type f angle is its supplement? Justify yur answer. 6. Determine whether r nt the cmplement f an angle can be btuse. Justify yur answer. Sectin 3 Tpic 2

9 9 7. Cnstruct AB and label midpint P n AB. Then, cnstruct PQ. Use the space prvided belw. Part A: What is the measure f QPA? Part B: What is the measure f QPB? Part C: QPA is acute btuse right straight and QPB is acute. btuse. right. straight. 8. Circle the best answer that cmpletes each statement belw. Justify yur answer under each statement with an example r cunter example. The sum f tw acute angles always smetimes never results in an btuse angle. Tw btuse angles are always smetimes never supplementary. The sum f tw right angles always smetimes never results in a straight angle. Sectin 3 Tpic 2

10 Name 10 Date Angles Angle Pairs Part 1 Independent Practice 1. Cnsider the figure belw. 4 5 l ( l ) Which f the fllwing statements are crrect? Select all that apply. 1 and 4 are adjacent angles. 1 and 2 are cmplementary angles. 3 and 4 are adjacent angles and cmplementary angles. 5 is a vertical angle t the cmbinatin f 3 and 2. 1 and 3 are vertical angles. 4 and 5 are adjacent angles, supplementary angles, and frm a linear pair. There is at least ne angle bisectr in the abve graph. Sectin 3 Tpic 3

11 11 2. Which f the fllwing figures display an angle bisectr? A B C D Suppse that MAP and MAC are linear pairs, m MAP = 7x 13 and m MAC = 3x Part A: Identify the line and the rays that frm MAP and MAC. Part B: Determine m MAP. Part C: Determine m MAC. Sectin 3 Tpic 3

12 12 4. Suppse that COP and TOD are vertical angles, m COP = 11x 17 and m TOD = 9x Part A: Cnstruct COP and TOD. [Hint: COD is an adjacent angle t COP and POT is an adjacent angle t TOD.] Part B: Determine m COD and m POT. 5. Suppse that LAP and LAR are adjacent angles, m LAP = 3x + 7, m LAR = 4 x 4, and m PAR = 2 3x + 7. Part A: Determine m LAP and m LAR. Part B: What can yu cnclude abut AL? Justify yur answer. 6. Is the perpendicular bisectr f a line segment als an angle bisectr? Justify yur answer. Sectin 3 Tpic 3

13 13 7. Cnsider the figure belw. (44x + 125y) A 225y 2 B l ( l ) The angle measures are represented by algebraic expressins. Determine the values f x, y, and z. Sectin 3 Tpic 3

14 Name 14 Date Angles Angle Pairs Part 2 Independent Practice 1. Cmplete the fllwing tw-clumn prf that prves the Cngruent Supplements Therem. x y z Given: x and y are supplements and y and z are supplements. Prve: x z Statements Reasns 1. x supplement t y m x + m y = y supplement t z m y + m z = m x + m y = m y + m z m x = m z x z 7. Sectin 3 Tpic 4

15 15 2. Cnsider the figure belw Given: 2 and 3 frm a linear pair, 1 and 3 are vertical angles, and m 1, m 4, and m 5 frm a straight angle. Prve: m 2 = m 4 + m 5 Statements Reasns Sectin 3 Tpic 4

16 16 3. If m TRI + m CRE = 180 and TRI CRE, what can yu cnclude abut m TRI and m CRE? Justify yur answer with a paragraph prf. 4. RIO and RIE are supplementary. One angle measures three times the ther angle. What is the cmplement f the smaller angle? 5. The measure f an angle is five degrees greater than six times its supplement. What is the measure f the larger angle? Sectin 3 Tpic 4

17 17 6. Write a plan and a tw-clumn prf t prve the Cngruent Cmplements Therem using the figure belw. A C M Q P B N O R Plan: Statements Reasns Sectin 3 Tpic 4

18 Name 18 Date Angles Special Types f Angle Pairs Frmed by Transversals and Nn-Parallel Lines Independent Practice 1. Classify the pair f the numbered angles. Select the crrect chice under each figure Alternate Exterir Angles Alternate Interir Angles Crrespnding Angles Cnsecutive Interir Angles Alternate Exterir Angles Alternate Interir Angles Crrespnding Angles Cnsecutive Interir Angles Alternate Exterir Angles Alternate Interir Angles Crrespnding Angles Cnsecutive Interir Angles Alternate Exterir Angles Alternate Interir Angles Crrespnding Angles Cnsecutive Interir Angles Sectin 3 Tpic 5

19 19 2. Identify the relatinship between each pair f angles, if any Pair f Angles Relatinship Pair f Angles Relatinship 1 and 7 4 and 6 1 and 8 4 and 7 2 and 4 5 and 4 3 and 5 8 and 5 3 and 8 8 and 7 3. Identify at least ne pair f the fllwing angles. Alternate Exterir Angles: a c b d e g f h Alternate Interir Angles: Cnsecutive Interir Angles: Crrespnding Angles: Linear Pairs: Vertical Angles: Sectin 3 Tpic 5

20 20 4. Cnsider the figure belw. t l 5 a c b d f e g h l 6 Which f the fllwing statements is true? a and c lie n the same side f the transversal and frm a linear pair. a and d are ppsite sides f the transversal and frm a pair f alternate interir angles. a, b, g and h are are exterir angles. b and h lie n the same side f the transversal and frm a pair f alternate exterir angles. d and f are cnsecutive interir angles lying n the same side f the transversal. e and f are adjacent angles and frm a vertical pair f angles. g and h are supplementary angles and n ppsite sides f the transversal. 5. Determine whether the fllwing statements are true r false. If there is a false statement, then make it a true statement. Statement True r False? Vertical angles are ppsite angles with the same vertex. True False Cnsecutive interir angles have crrespnding psitins in the same side f the transversal. True False Alternate exterir angles are angles n alternate sides and between the tw parallel r nn-parallel lines. True False A linear pair are adjacent angles that make a straight line. True False Sectin 3 Tpic 5

21 21 6. Cnsider the figure belw. Park Day Care Museum $ Cffee Shp Cmmunity Center Wrship Center $ Bank Fire Statin Match the angles n the left with their crrespnding names n the right. Write the letter f the mst apprpriate answer beside each angle pair belw. Museum and Wrship Center A. Alternate Interir Angles Bank and Day Care B. Cnsecutive Interir Angles Park and Cffee Shp C. Crrespnding Angles Fire Statin and Wrship Center D. Vertical Angles Cmmunity Center and Day Care E. Alternate Exterir Angles Bank and Museum F. Linear Pair Sectin 3 Tpic 5

22 Name 22 Date Angles Special Types f Angle Pairs Frmed by Transversals and Parallel Lines Part 1 Independent Practice 1. Cnsider the figure belw. r % r ' l % l ' Which lines f the fllwing segments are parallel? Justify yur answer. 2. Cnsider the figure belw. r % r ' l % l ' 117 Which lines f the fllwing segments are parallel? Justify yur answer. Sectin 3 Tpic 6

23 23 3. Cnsider the figure belw, where l % and l ' are parallel and cut by transversals t % and t '. t % t ' l % l ' Part A: What is the relatinship between 1 and 3? Justify yur answer. Part B: What is the relatinship between 2 and 7? Justify yur answer. Part C: What is the relatinship between 4 and 6? Justify yur answer. Part D: What is the relatinship between 11 and 15? Justify yur answer. Part E: What is the relatinship between 12 and 13? Justify yur answer. Part F: What is the relatinship between 14 and 15? Justify yur answer. Sectin 3 Tpic 6

24 24 4. Cnsider the figure belw. P A B 2a 9 Q R C 5a + 14 D S Part A: Slve fr a and justify yur answer. Part B: Determine m ABQ. Part C: Determine m BCR. 5. Write the cnverse f the statement belw. Then determine whether the statement is true r false. If false, give a cunterexample. Cnditinal Statement: If tw angles are crrespnding, then they are cngruent. Sectin 3 Tpic 6

25 25 6. Cnsider the figure belw. F M 7a + 50 N G J T 14a 20 U K Part A: Slve fr a and justify yur answer. Part B: Determine m FNT. Part C: Determine m KTU. 7. Cnsider the fllwing cnditinal statement: If tw angles are supplementary, then they are frmed by tw parallel lines cut by a transversal. Which f the fllwing is a cunterexample t this statement? A B C D Sectin 3 Tpic 6

26 Name 26 Date Angles Special Types f Angle Pairs Frmed by Transversals and Parallel Lines Part 2 Independent Practice 1. Cnsider the figure belw. W U Z X 113 H 95 T S Q D B V Y Part A: Determine m VHT. Part B: Determine m QTS. Part C: Determine m ZHQ. Sectin 3 Tpic 7

27 27 2. Cnsider the figure belw. L S 110 A M E C H 34 V I K B E Part A: Determine m MIH. Part B: Determine m AVM. Part C: Determine the measure f the btuse angle frmed at the intersectin f AV and HI. Sectin 3 Tpic 7

28 28 3. Cnsider the fllwing diagram n the right. t > 1 Given: l > t > and m 1 = l > Prve: m 3 = 57 Cmplete the tw-clumn prf belw. Statements Reasns Cnsider the figure belw where MN PQ, m PTS = (19x + 5) and m NST = (17x + 15). Determine m MSR and m STQ. R N M S Q T P U Sectin 3 Tpic 7

29 29 5. Cnsider the fllwing diagram. A G M 107 E N B W C F R S D 32 H Given: AB CD, m MNE = 107 and m DSH = 32. Prve: m MWR = 105 Cmplete the tw-clumn prf belw. Statements Reasns Sectin 3 Tpic 7

30 Name 30 Date Angles Perpendicular Transversals Independent Practice 1. Cnsider the lines and the transversal drawn in the crdinate plane belw. t l, 1 l - 2 Part A: Prve that 1 2. Justify yur wrk. Part B: Prve that m 1 = m 2 = 90. Justify yur wrk. Sectin 3 Tpic 8

31 31 2. Cnsider the figure belw. t - 1 l, 2 l - Part A: If l, l -, then use the Perpendicular Transversal Therem t prve that 1 2. Write yur answer in a paragraph prf. Part B: Suppse yur friend als prved crrectly that 1 2. The difference is that yur friend did nt use the Perpendicular Transversal Therem. Determine hw yur friend was able t prve the same statement using a different apprach. Sectin 3 Tpic 8

32 32 3. Cnsider the figure belw. t, t - l, 1 2 l Given: m 1 = 52, m 2 = 90, and m 3 = 90 Prve: m 5 = 128 Cmplete the fllwing tw-clumn prf. Statements Reasns Sectin 3 Tpic 8

33 33 4. Cnsider the figure belw. l, l p q Assume that l, p, l, q, m 6 = (5x + 4) and m 8 = (10x 19). Part A: Determine the value f x. Part B: Prve theretically and algebraically that m 4 + m 7 = Sectin 3 Tpic 8

34 Name 34 Date Angles Angle-Preserving Transfrmatins Independent Practice 1. Cnsider the figure belw in which l " l $. t m n Part A: Determine the angles that are cngruent with 6 after 6 has been translated eight units t the right and tw units dwn. Justify yur answer. Part B: Determine the angles that are supplementary with 3 after 3 has been rtated 180 clckwise. Part C: Explain the effect that reflecting the figure abve acrss the line y = x may have n 1, 2, 3, 4, 5, 6, 7, and 8. Sectin 3 Tpic 9

35 35 2. Cnsider the fllwing figure. P M N R A O B Part A: Reflect the abve image acrss the y-axis and sketch it n the crdinate plane. Part B: Write a paragraph prf t prve that after the reflectin, m NOA = m N O A. Sectin 3 Tpic 9

36 36 3. Cnsider the transfrmatin that yu did in exercise #2 and dilate the image centered at the rigin with a scale factr f ". Sketch the new image in the $ crdinate plane belw. Explain the angle measures after the dilatin. 4. Cnsider the image in Quadrant I and the pre-image in Quadrant II a e b c f g d h If m 4 = 5x + 14 and m e = 7x 2, then m 1 = and m c =. Sectin 3 Tpic 9

37 37 5. The figure in Quadrant IV f the crdinate plane belw is a transfrmatin f the figure in Quadrant II. A E B F C G D H Part A: What type f transfrmatin is shwn abve? Justify yur answer. Part B: Write a paragraph prf t prve that 3 C and that 3 is a supplement angle t E. Sectin 3 Tpic 9

38 38 6. The figure in Quadrant I f the crdinate plane belw is a transfrmatin f the figure in Quadrant IV. E F G H A B C D Part A: What type f transfrmatin is shwn abve? Justify yur answer. Part B: Write a paragraph prf t prve that H and 1 are cngruent. Sectin 3 Tpic 9

39 39 7. The figure in Quadrant III f the crdinate plane belw is a transfrmatin f the figure in Quadrant II a e b c f g d h Part A: What type f transfrmatin is shwn abve? Justify yur answer. Part B: If m c = 5x 1, m f = 11y + 3, m 1 = 8x 1, and m 8 = 17y + 9, then determine: x = y = m 6 = m a = Sectin 3 Tpic 9