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Name________________________________________________Period_____Date__________________ Hon Geometry Midterm Review Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. One way to show that two triangles are similar is to show that ______. a. two angles of one are congruent to two angles of the other b. two sides of one are proportional to two sides of the other c. a side of one is congruent to a side of the other d. an angle of one is congruent to an angle of the other ____ 2. For the figure shown, which statement is not true? a. b. c. d. ____ 3. Choose the statement that is NOT ALWAYS true. For a rhombus ________. a. each diagonal bisects a pair of opposite angles b. all four sides are congruent c. the diagonals are congruent d. the diagonals are perpendicular ____ 4. Which statement is false? a. If a quadrilateral is a square, then it is not a kite. b. Some parallelograms are rhombuses. c. All parallelograms are quadrilaterals. d. If a quadrilateral is a rectangle, then it is a kite. Numeric Response 1. Armando lives on one end of a street with a newsstand on the other. Armando picks up newspapers at the newsstand and then delivers them to 14 equally-spaced houses on his way back. He travels from the newsstand to the first house, then delivers a newspaper to each house. At the end of his route, he continues GRZQWKHVWUHHWDQGJRHVKRPH)LQGWKHGLVWDQFHIURPWKHODVWKRXVHWR$UPDQGR¶VKRPH Event $UPDQGR¶V newspaper delivery route Distance from Newsstand to $UPDQGR¶V Home Distance from Newsstand to First House Distance Between Houses Distance from Last House to $UPDQGR¶V Home 340 m 30 m 20 m ? Name________________________________________________Period_____Date__________________ 2. The supplement of an angle is 26 more than five times its complement. Find the measure of the angle. 3. Find the value of x so that . m (6x + 5)º (5x - 12)º n 4. Find the value of x. (2.5x + 6)o Short Answer 1. Name a plane that contains . R W C A T 2. D is between C and E. C = D 4x + 8 6x , = 27 , and DE = 27. Find CE. E Name________________________________________________Period_____Date__________________ 3. Find the measure of . Then, classify the angle as acute, right, or obtuse. C D B O 4. m and m A . Find m . I L K J 5. bisects ,m 6. Tell whether , and m and . Find m . are only adjacent, adjacent and form a linear pair, or not adjacent. F B 1 A 2 3 4 C G 7. Use the Distance Formula and the Pythagorean Theorem to find the distance, to the nearest tenth, from T(4, ± 2) to U(±2, 3). Name________________________________________________Period_____Date__________________ 8. Name all pairs of vertical angles. J M L K N 9. Find the coordinates of the midpoint of with endpoints C(1, ±6) and M(7, 5). y 8 6 M 4 2 ± ± ± ± 2 4 6 8 x ± ± ± C ± 10. Name three collinear points. P G N R 11. Identify the property that justifies the statement. and . So . 12. Write a justification for each step, given that E F G . H Given information [1] Segment Addition Postulate [2] Subtraction Property of Equality Name________________________________________________Period_____Date__________________ 13. Write a two-column proof of the statement . Given: AB = CD; BF = FC Prove: A B F C D Two-column proof: Statements 1. ; 2. [1] 3. [2] 4. 5. 14. Write a two-column proof. Given: m + m = 90 , m Reasons 1. Given 2. Addition Property of Equality 3. Segment Addition Postulate 4. Substitution 5. Definition of congruent segments +m = 90 , m =m 4 3 2 1 Prove: m =m Complete the proof. Proof: 1. m 2. [1] 3. m 4. m 5. m 6. m +m +m =m +m =m Statements = 90 =m +m =m +m Reasons 1. Given 2. Given 3. Substitution Property 4. Given 5. [2] 6. [3] Name________________________________________________Period_____Date__________________ 15. Write a flowchart proof. Given: Prove: 1 2 3 4 Complete the proof. Flowchart proof: Given [1] Definition of linear pair [2] Definition of congruent segments 16. Write a two-column proof. B 1 3 2 A Given: Prove: C is a right angle. are complementary. Complete the proof. Two-column proof: Statements 1. is a right angle. 2. m 3. 4. 5. 6. 7. are complementary. Reasons 1. Given 2. Definition of a right angle 3. [1] 4. Substitution 5. [2] 6. Substitution 7. Definition of complementary angles Name________________________________________________Period_____Date__________________ 17. Identify the transversal and classify the angle pair n m 1 2 3 4 9 10 5 6 l 8 18. Find m 12 11 7 . >> A xº C (3x - 70)º >> B 19. Find m . R >> U [± T S (3x)º >> V and . Name________________________________________________Period_____Date__________________ 20. Violin strings are parallel. Viewed from above, a violin bow in two different positions forms two transversals to the violin strings. Find x and y in the diagram. 100º (4x + y)º (8x + y)º 60º 21. Use slopes to determine whether the lines are parallel, perpendicular, or neither. 22. Use the information show that . , and the theorems you have learned to l 1 2 23. Find m in the diagram. (Hint: Draw a line parallel to the given parallel lines.) >> ) ) 1 >> Name________________________________________________Period_____Date__________________ 24. Write a two-column proof. Given: Prove: t 1 2 m l Complete the proof. Proof: Statements Reasons 1. [1] 2. 3. 1. Given 2. [2] 3. [3] 25. Write the equation of the line with slope 2 through the point (4, 7) in point-slope form. 26. Determine whether the lines and are parallel, intersect, or coincide. 27. Use the slope formula to determine the slope of the line. y 8 6 4 2 ± ± ± ± ± 2 4 6 x 8 ± A ± B ± 28. Graph the line 29. Classify . by its angle measures, given m D 25º 60º A 75º B C ,m , and m . Name________________________________________________Period_____Date__________________ 30. Classify by its side lengths. A 8 B C 8 31. is an isosceles triangle. is the longest side with length . = and = . Find . 8 x+ 5 A B 3 x +9 4x+ 4 C 32. Daphne folded a triangular sheet of paper into the shape shown. Find , and m . E D C A 61º 42º 22º B , given , Name________________________________________________Period_____Date__________________ 33. Given: Identify all pairs of congruent corresponding parts. A M B C 34. Given: O N , , . T is the midpoint of . R S T U Prove: Complete the proof. Proof: Statements Reasons 1. 2. and are right angles. 3. 4. 5. 6. 7. T is the midpoint of . 8. 9. 10. 35. . B to C to D to E. and B are equilateral. D C A G F 1. Given 2. [1] 3. Right Angle Congruence Theorem 4. Given 5. [2] 6. Given 7. Given 8. Definition of midpoint 9. [3] 10. Definition of congruent triangles E and . Find the total distance from A to Name________________________________________________Period_____Date__________________ 36. Given the lengths marked on the figure and that bisects , use SSS to explain why . 4 cm E A 3 cm 3 cm D 4 cm C B 37. The figure shows part of the roof structure of a house. Use SAS to explain why . R || S || T U Complete the explanation. It is given that [1]. Since and are right angles, [2] by the Right Angle Congruence Theorem. By the Reflexive Property of Congruence, [3]. Therefore, by SAS. 38. Use AAS to prove the triangles congruent. Given: , Prove: 'ABC 'HGF , G > >> A > F C | | H >> B Proof: Given 1. 'ABC 'HGF Given 2. AAS Name________________________________________________Period_____Date__________________ 39. Determine if you can use the HL Congruence Theorem to prove 'ACD 'DBA. If not, tell what else you need to know. P A B | ^ ^ | C D Q 40. For these triangles, select the triangle congruence statement and the postulate or theorem that supports it. L J K B A C Name________________________________________________Period_____Date__________________ 41. Given: Prove: , bisects F B ) C ) A D G Complete the flowchart proof. Proof: Given bisects Given. 1. 2. 'ACB 'ACD Definition of angle bisector. 4. 5. 3. 42. Given: A(3, ±1), B(5, 2), C(±2, 0), P(±3, 4), Q(±5, ±3), R(±6, 2) Prove: Complete the paragraph proof. , 'ABC >@ by [4], and , and . So by [5]. , , and . Therefore Name________________________________________________Period_____Date__________________ 43. Write an equation for the line parallel to the line shown that passes through the point (±2, 3). y 5 4 3 2 1 ± ± ± ± ± ± 1 2 3 4 x 5 ± ± ± ± 44. Find CA. A ) s+ 2 ) ) C 2 s 10 B 45. Find the measure of each numbered angle. > | | 3 1 R 117 2 > 46. Given that bisects Y X Z W and , find . Name________________________________________________Period_____Date__________________ 47. Vanessa wants to measure the width of a reservoir. She measures a triangle at one side of the reservoir as shown in the diagram. What is the width of the reservoir (BC across the base)? 120 m B X 120 m A 150 m 100 m Y 100 m C 48. If two polygons are SIMILAR, then the corresponding sides must be _____. 49. The perimeter of 'PQR is 80, PQ = 30, 'PQR a'STU, and ST = 18. What is the perimeter of 'STU? 50. Two ladders are leaning against a wall at the same angle as shown. How far up the wall does the shorter ladder reach? 51. Triangles LMN and NWR are right triangles. What is the length of Name________________________________________________Period_____Date__________________ 52. The postulate or theorem that can be used to prove that the two triangles are similar is _____. 53. Consecutive angles in a parallelogram are always ________. 54. Find the value of the variables in the parallelogram. 55. (2, 3) and (3, 1) are opposite vertices in a parallelogram. If (0, 0) is the third vertex, then the fourth vertex is _____. 56. Isosceles trapezoid JKLM has legs find the value of x. and , and base If and 57. For the trapezoid shown below, the measure of the midsegment is _______. 58. Use slope or the Distance Formula to determine the most precise name for the figure: A(±1, ±4), B(1, ±1), C(4, 1), D(2, ±2). Name________________________________________________Period_____Date__________________ 59. In the diagram, is similar to . Write the statement of proportionality. 60. In and In triangles are similar, and if so, write a similarity statement. 61. Given: . Find the length of . 62. Find the value of x to one decimal place. The polygons in each pair are similar. Find the value of each variable. 63. and State whether the Name________________________________________________Period_____Date__________________ 64. Find the sum of the measures of the interior angles in the figure. 65. Find the number of sides of a convex polygon if the measures of its interior angles have a sum of 2880°. 66. Find AM in the parallelogram if and 67. If the diagonals of a parallelogram are perpendicular, then the parallelogram is also what type of figure? 68. In what type of trapezoid are the base angles congruent? Performance Task: 69. Draw a Venn diagram showing the relationships among the various types of quadrilaterals. Name________________________________________________Period_____Date__________________ Other 1. Complete the steps of this proof. Given: parallelogram WXYZ Prove: 2. Given: # and Prove: VX = XT V U X S T Name________________________________________________Period_____Date__________________ 3. Use the distance formula to determine whether ABCD below is a parallelogram. Name________________________________________________Period_____Date__________________ Hon Geometry Midterm Review Answer Section MULTIPLE CHOICE 1. 2. 3. 4. A B C D NUMERIC RESPONSE 1. 2. 3. 4. 50 74 17 21.6 SHORT ANSWER 1. 2. 3. 4. 5. 6. 7. 8. plane WRT CE = 105 m ; right m m = 20° only adjacent 7.8 units ; 1 9. (4, 2 ) 10. R, G, and N 11. Transitive Property of Congruence 12. [1] Segment Addition Postulate [2] Substitution Property of Equality 13. [1] [2] 14. [1] m + m = 90 [2] Substitution Property [3] Subtraction Property of Equality 15. [1] and are supplementary; and are supplementary [2] Congruent Supplements Theorem 16. [1] Angle Addition Postulate [2] Definition of congruent angles 17. The transversal is line l. The angles are corresponding angles. 18. m = 35° 19. m = 20. Name________________________________________________Period_____Date__________________ 21. neither 22. By substitution, and By the Substitution Property of Equality, . By the Converse of the Alternate Interior Angles Theorem, 23. = 135° 24. [1] [2] 2 intersecting lines form linear pair of s lines . [3] 2 lines to the same line lines . 25. 26. intersect 2 27. 3 28. y 12 10 8 6 4 2 ± ± ± ± ± 2 4 6 8 10 12 x ± ± ± 29. obtuse triangle 30. equilateral triangle 31. = 45 32. = 33. , , , 34. [1] Definition of perpendicular lines [2] Third Angles Theorem [3] Reflexive Property of Congruence 35. 98 36. 37. [1] [2] [3] 38. 1. Alternate Interior Angles Theorem 2. Alternate Exterior Angles Theorem 39. Yes. 40. , HL 41. 1. Congruent Supplements Theorem 2. 3. Reflexive Property of Congruence , , . . Name________________________________________________Period_____Date__________________ 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 4. AAS 5. CPCTC [1] PQ [2] [3] 'RPQ [4] SSS [5] CPCTC y = 3x ± 3 CA = 14 m = ,m = 300 m proportional 48 18 ft 15.6 cm AA Similarity Postulate supplementary angles x = 21°, y = 55°, z = 104° 11 2 57. 29 58. rhombus 56. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. ,m not similar 40 4.7 x = 12, y = 6 540° 18 9.5 A rhombus an isosceles trapezoid = Name________________________________________________Period_____Date__________________ OTHER 1. 2. 3. Since AB = CD = and BC = AD = 8, ABCD is a parallelogram.