Indicate whether the statement is true or false.Indicate whether the statement is true or false. 1....

.

Indicate whether the statement is true or false.

1. The bearing of the airplane with the path shown is N 30° E. a. True

b. False

2. If M and N are the midpoints of nonparallel sides and of trapezoid HJKL, then .

a. True

b. False

3. For a rectangle with base length of 1 foot and height 6 inches, the area is 6 . a. True

b. False

4. Given that quadrilateral quadrilateral MNPQ, . a. True

b. False

5. The region bounded by radii and and arc is known as a secant of the circle. a. True

b. False

6. The lateral area L of any prism whose altitude measures h and whose base has perimeter P is given by L = hP. a. True

b. False

7. If ray BD bisects , then . a. True

b. False

8. In a prism, the two bases are parallel to each other and congruent to each other. a. True

b. False

.

9. If a lateral edge is perpendicular to a base edge, then the prism shown is a regular triangular prism. a. True

b. False

10. With the circle inscribed in , it follows that AR = AS, BS = BT, and CR = CT. a. True

b. False

11. If AB = 3 and BC = 4 in rectangle ABCD, then the length of diagonal is 5. a. True

b. False

12. Given that , it follows that . a. True

b. False

13. The formula for the volume of a right circular cylinder of radius r and altitude h is given by . a. True

b. False

14. An octagonal prism has 9 faces. a. True

b. False

15. Two circles that are internally tangent have three common tangent lines. a. True

b. False

16. If and are complementary, then each of these angles 1 and 2 is acute. a. True

b. False

17. A pentagon has the same number of diagonals as it has sides. a. True

b. False

18. Both the kite and the parallelogram have two pairs of congruent angles. a. True

b. False

.

19. One of the methods for proving that two triangles are congruent is abbreviated AAA. a. True

b. False

20. If , then . a. True

b. False

Indicate the answer choice that best completes the statement or answers the question.

21. Suppose that you have utilized congruent vertical angles to prove that

by the method SAS. By what reason can you, in turn, state that ?

a. Identity b. SAS

c. CPCTC d. Definition of midpoint

22. In the circle, m = 68° and m = 74°. Find m . a. 34° b. 37°

c. 71° d. 142°

.

23. In , m = 60° and BC = 12. Find AB. a. 3 b. c. 6 d.

24. In isosceles triangle RST, . If , , and the perimeter of is 36, find the value of x. a. x = 5.5 b. x = 6

c. x = 6.5 d. None of These

25. Point P lies in the exterior of so that is tangent to the circle. Also, is a secant that intersects at B and C, where P-B-C. If PB = 9 and BC = 7, find PA. a. 10 b. 12

c. 16 d. None of These

26. Suppose that . Which must be true?

a. a || b b. a ⊥ c

c. c || d d. c is not parallel to d

27. Find the area of a regular hexagon whose sides measure 6 inches each. a. 9 b. 9

c. 54 d. 54

28. is an altitude for . If RV = 5, RS = 7, and WT = 4, find the length of altitude . a. 3 b. 3.5

c. 4 d. None of These

29. In , m = 103° and m = 77°. Which statement is false?

a. is a semicircle b. would be a diameter

c. is a minor arc d. would be a right angle

.

30. Consider regular pentagon ABCDE. If diagonal is drawn, then a quadrilateral ACDE is formed. Being as specific as possible, what type of quadrilateral is ACDE?

a. parallelogram b. kite

c. trapezoid d. isosceles trapezoid

31. If the diagonals of a rhombus measure 10 cm and 24 cm, what is the perimeter of the rhombus?

a. 13 cm b. 34 cm

c. 52 cm d. 68 cm

32. Which statement would one prove by the indirect method?

a. If and are not congruent angles, then and are not vertical angles. b. If r || s, then . c. If l ⊥ m and m ⊥ p, then l || p. d. If two sides of a triangle are congruent, then two angles of that triangle are congruent.

33. Which type of triangle has sides of lengths a = 8, b = 15, and c = 17?

a. acute b. right c. obtuse d. No triangle with these lengths of sides exists.

34. For the right triangular prism shown, the base is a right triangle with sides of lengths 3 in, 4 in, and 5 in. If the prism has a height of 6 inches, find its volume. a. 24 b. 36

c. 72 d. 360

35. Where C is the circumference of a circle and r is its length of radius, the approximate value of the ratio C : r is: a. 1.57 b. 3.14

c. 6.28 d. 12.56

36. Find the sum of the interior angles of a hexagon. a. 180° b. 360°

c. 540° d. None of These

37. Given lines and m with , it follows that: a. b.

c. d. None of These

38. Find the measure of each interior angle of a regular octagon. a. 45° b. 108°

c. 120° d. 135°

.

39. has been constructed tangent to at point T and to at point W. How are radii and related?

a. congruent b. congruent and parallel c. parallel d. None of These

40. The midpoints of the sides of rhombus ABCD are joined in order to form quadrilateral MNPQ. Being as specific as possible, what type of quadrilateral is MNPQ?

a. parallelogram b. rectangle

c. square d. rhombus

41. In rectangle ABCD, , , and . Find the value of x.

42. In the figure, bisects and D is the midpoint of . If and , find the value of x.

43. Given that , what angle of is congruent to of ?

44. For , radii and and arc bound a sector. If m = 100° and PX = 5.6 inches, find the area of the sector correct to the nearest tenth of a square inch.

.

45. In the figure, and bisect each other. If and is larger than , find .

46. In rhombus MNPQ, diagonal is congruent to side . Find m .

47. When the midpoints of the sides of a square RSTV are joined in order, quadrilateral MNPQ is formed. Being as specific as possible, what type of quadrilateral is MNPQ?

48. In addition to being congruent, how are the diagonals of a square related?

49. Find the measure of the angle formed by the hands of a clock at exactly 4:10 PM.

50. If m = 45° and OA = 4.3 cm, find l correct to the nearest tenth of a centimeter.

51. Points A, B, and C are collinear. If AB = 12 and BC = 7, find the two possible lengths of .

52. In the figure, S-T-U-V and . Draw a conclusion regarding and .

.

53. A pyramid has a square base with sides of length e. If the altitude of the pyramid also measures e, what is the volume of the pyramid?

54. Quadrilateral ABCD quadrilateral HJKL. If , , , and

, find x. 55. Each base edge of a regular pentagonal pyramid measures 10 cm. If the lateral area of this pyramid is 425 , find the length of the slant height of the pyramid.

56. What is the name of this property? If , then .

57. Find the length of base in an isosceles triangle with perimeter 25 inches and length of leg 8 inches.

58. In rectangle ABCD, AB = 5 and BC = 4. As a square root, find the length of diagonal .

59. Let point E lie in the exterior of . How many tangent lines can be constructed to from point E?

60. In , chord diameter . With chords and , quadrilateral RSTV is formed. Being as specific as possible, what type of quadrilateral is RSTV?

61. In isosceles triangle RST with vertex angle S, . Describe the measure of .

62. Use to find the exact total area of the right circular cone for which r = 3 cm and l = 5 cm.

63. For , E lies on side so that . For , what name is given to the line segment ?

64. The measures of the three interior angles of a triangle are x, 2x, and 3x. What type of triangle is the triangle described?

65. Find the measure of each exterior angle of a regular dodecagon (polygon with 12 sides).

66. In , m = 90°. What fraction represents the part of the circumference that is the length of ?

67. In , diagonals and intersect at point T. If MN = 12.5, NP = 8.7, and QN = 14.6, find QT.

.

68. In this figure, and are complementary. Also, and are complementary. Regarding and , what

conclusion may you draw?

69. In , the length of radius is 6 inches. If m = 90° and m = 60°, how much longer is chord than chord

?

70. A storage tank is in the shape of a right circular cylinder. If r = 3 ft and h = 4 ft,find the exact volume of the cylinder.

71. One property of proportions takes the form, “If , then .” Use this property to complete this statement.

Because , it follows that:

72. In the proof that , what statement can you justify by the reason Identity?

73. The figure shows right triangle ABC with . Also, . Where , , , , and , what reason allows you to conclude that ?

74. For the segment shown, let the center of the circle be point O. If the area of the related sector bounded by and and arc is 45 while the area of is 28 , find the area of the segment bounded by and .

75. You have proved that by the reason ASA and in turn that by CPCTC. What reason allows you to further conclude that “Z is the midpoint of ?”

.

76. In isosceles triangle RST, . If , find the length of . 77. The total area of a right circular cylinder is . If the height of the cylinder is 4,find the length of the radius.

78. For trapezoid MNPQ, . Also, A is the midpoint of while B is the midpoint of . If , , and , find the value of x.

79. A triangle has a perimeter of 40 and area of 60. Using A = rP, find the length of radius r for the inscribed circle for this triangle.

80. Given a regular square pyramid, with respect to which figure(s) does this pyramid have symmetry . . . a point, a line, or a plane?

81. Provide missing statements and missing reasons for the proof of the theorem, “If two sides of a triangle are congruent, then the angles opposite those sides are also congruent.” Given: with Prove: S1. R1. S2. Draw the angle bisector for R2. Every angle has exactly one angle-bisector. S3. R3. S4. R4.

82. Where is the degree measure for the arc of a sector of a circle, the ratio of the area of the sector to that of the area of

the circle is given by . Use this ratio to explain why

the area of the sector is given by .

.

[Note: In the figure, the sector with arc measure is bounded by radii , , and .]

83. Supply missing statements and missing reasons for the following proof. Given: so that bisects ; also, Prove: S1. so that bisects R1. S2. R2. S3. R3. Given S4. R4. If 2 angles of one triangle are congruent to 2 angles of a second triangle, then the third angles of these triangles are also congruent.

84. Provide all statements and all reasons for this proof. Given: with ;

with Prove:

.

85. Supply missing statements and missing reasons for the following proof. Given: in Prove: is an isosceles triangle S1. R1. S2. R2.

S3. R3. S4. ? and ? R4. The degree measure of an iscribed angle is equal to one-half the degree measure of its intercepted arc. S5. R5. S6. R6. Definition of congruent angles S7. R7. If two angles of a triangle are congruent, then the two sides that lie opposite those angles are also congruent. S8. R8.

86. Use the drawing provided to explain the 45 -45 -90 Theorem. “In a triangle whose angles measure 45 , 45 , and 90 , the hypotenuse has a length equal to the product of and the length of either leg.” Given: with , , and Prove: and

87. Supply missing statements and missing reasons for the following proof.

.

Given: Rectangle MNPQ with diagonals and Prove: S1. R1. S2. and are rt. R2. S3. R3. S4. R4. The diagonals of a rectangle are congruent. S5. R5.

88. Provide the missing statements and missing reasons for the following proof. Given: and V is the midpoint of Prove: S1. R1. S2. R2. S3. R3. Given S4. R4. S5. R5. Identity S6. R6. S7. R7.

89. Provide mssing statements and missing reasons for the proof of the theorem, “Corresponding altitudes of congruent triangles are congruent.” Given: ; and Prove: S1. R1. S2. and R2. S3. R3. Given S4. and are rt. R4. S5. R5. All right angles are congruent. S6. R6. S7. R7.

.

90. Supply missing reasons for this proof. Given: m || n Prove: S1. m || n R1. S2. R2. S3. R3. S4. R4.

91. Supply missing statements and reasons for the following proof. Given: and intersect at point X Prove: S1. R1. S2. and are supp. R2. S3. R3. If the exterior sides of two adjacent angles form a straight line, these angles are supplementary. S4. R4. Two angles that are supplementary to the same angle are congruent.

92. Use the drawing(s) to explain the 30 -60

.

-90 Theorem. “In a triangle whose angles measure 30 , 60 , and 90 , the hypotenuse has a length equal to twice the length of the shorter leg, and the length of the longer leg is the product of

and the length of the shorter leg.” Given: Right with , , and ; also, Prove: and

93. Supply missing statements and missing reasons for the following proof. Given: ; V is the midpoint of and W is the midpoint of . Prove: S1. R1. S2. and R2. Definition of midpoint S3. and R3. S4. R4. Substitution Property of Equality S5. R5. S6. R6. 94. Supply all statements and all reasons for the following proof. Given: ; M is the midpoint of and N is the midpoint of Prove: MNAB is a trapezoid

.

95. Provide missing reasons for the proof of the theorem, “A diagonal of a parallelogram separates it into two congruent triangles.” Given: with diagonal Prove:

S1. with diagonal R1. S2. R2. S3. R3. S4. R4. S5. R5. S6. R6. S7. R7.

96. Explain (prove) the following property of proportions. “If (where and ), then .”

97. Explain why the following must be true. Given: Points A, B, and C lie on in such a way that ; also, chords , , and (no drawing provided) Prove: must be an isosceles triangle. 98. Supply missing statements and missing reasons for the following proof. Given: ; chords and intersect at point V Prove: S1. R1. S2. Draw and . R2. S3. R3. Vertical angles are congruent. S4. R4. S5. R5. AA

S6. R6. S7. R7. Means-Extremes Property of a Proportion

.

99. Provide all statements and all reasons for the following proof. Given: , ,

, and Prove: Quad. ABCD is a parallelogram 100. Given: and are supplementary Prove: Supply missing statements and missing reasons for this proof. S1. and are supplementary R1. S2. R2. If the exterior sides of 2 adjacent angles form a straight line, the angles are supplementary. S3. R3. Two angles that are supplementray to the same angle are congruent.

.

Answer Key 1. True

2. True

3. False

4. True

5. False

6. True

7. True

8. True

9. False

10. True

11. True

12. False

13. True

14. False

15. False

16. True

17. True

18. False

19. False

20. True

21. c

22. c

23. d

24. b

25. b

26. a

27. c

.

28. c

29. c

30. d

31. c

32. a

33. b

34. b

35. c

36. d

37. b

38. d

39. c

40. b

41.

42. 29

43.

44. 27.4

45. 38°

46. 120°

47. a square

48. perpendicular-bisectors of each other

49. 65°

50. 3.4 cm

51. AC = 5 or AC = 19

52.

53.

.

54.

55. 17 cm

56. Means-Extremes Property

57. 9 inches

58.

59. 2

60. isosceles trapezoid

61.

62.

63. altitude

64. right

65. 30°

66.

67. 7.3

68. or m = m

69. inches

70.

71.

72.

73. CSSTP

74. 17

75. The definition of midpoint.

76.

77. 3 units

78. x = 4

79. 3

.

80. both line and plane

81. S1. with R1. Given R3. The bisector of the vertex angle of an isosceles triangle separates the triangle into two congruent triangles. S4. R4. CPCTC

82. Given that , it follows that . Where r is the length of radius of the circle, the area of the circle is given by . By substitution, it follows that

.

83. R1. Given

S2. R2. Definition of angle-bisector S3. S4.

84. S1. with R1. Given

S2. with R2. Given

S3. R3. Identity

S4. R4. SSS

85. S1. in R1. Given R2. Definition of congruent arcs R3. Multiplication (or Division) Property of Equality

S4. and

R5. Substitution Property of Equality S6.

S7. S8. is an isosceles triangle R8. Definition of isosceles triangle

86. In , . Thus, the sides opposite these angles are congruent. If , then With the right angle at C, we apply the Pythagorean Theorem to obtain

. Then , so . Applying the Square Roots Property, we have

or . Then .

87. S1. Rectangle MNPQ with diagonals and R1. Given R2. All angles of a rectangle are right angles. R3. Identity

S4.

S5. R5. HL

88. R1. Given

.

R2. Perpendicular lines form congruent adjacent angles. S3. V is the midpoint of R4. Definition of midpoint S5. R6. SAS S7. R7. CPCTC

89. R1. Given R2. CPCTC

S3. and R4. Perpendicular lines form right angles. S5. R6. AAS

S7. R7. CPCTC

90. R1. Given R2. If 2 parallel line are cut by a transversal, then corresponding angles are congruent. R3. If two lines intersect, the vertical angles formed are congruent. R4. Transitive Property of Congruence

91. S1. and intersect at point X R1. Given S3. and are supp. S4.

92. We reflect across to create an equiangular (and equilateral) triangle ( ). The reflection of , namely ) is conruent to . Then and by the Sement-Addition Postulate,

, so Knowing that is equilateral, we have (completing the first part of the proof). Using the Pythagorean Theorem in ,

or

, so or

(completing the final part of the proof)

93. S1. ; V is the midpoint of and W is the midpoint of . R1. Given R3. Division Property of Equality

S4. R5. Identity S6.

R6. SAS

94. S1. ; M is the midpoint of and N is the midpoint of R1. Given

S2. R2. The line segment that joins the midpoints of 2 sides of a triangle is parallel to the third side

.

of the triangle. S3. MNAB is a trapezoid R3. Definition of trapezoid

95. R1. Given R2. The opposite sides of a parallelogram are parallel (definition). R3. If 2 lines are cut by a trans, the alternate interior angles are congruent. R4. Same as reason 2 R5. Same as reason 3. R6. Identity R7. ASA

96. Given that , we add 1 to each side of this equation. By the Addition Property of Equality, . But and , so that by the Substitution

Property of Equality. In turn, .

97. Given that in , it follows that . But congruent arcs have congruent chords so that . Then must be an isosceles triangle.

98. S1. ; chords and intersect at point V R1. Given R2. Through 2 points, there is exactly one line. S3. R4. If 2 inscribed angles of a circle intersect the same arc, these angles are congruent. S5. R6. CSSTP

S7.

99. S1. , R1. Given

S2. R2. If 2 coplanar lines are to the same line, they are . S3. , and R3. Given

S4. R4. Same as reason 2. S5. Quad. ABCD is a parallelogram R5. Definition of parallelogram

100. R1. Given S2. and are supplementary. S3.

Indicate whether the statement is true or false.Indicate whether the statement is true or false. 1....

Documents

Transcript of Indicate whether the statement is true or false.Indicate whether the statement is true or false. 1....