NAME DATE PER. ACADEMIC GEOMETRY: SPRING SEMESTER REVIEW Find the indicated value in each of the following.

Transcription

1 NME DTE PER. CDEMIC GEOMETRY: SPRING SEMESTER REVIEW Find the indicated value in each of the following. 1. re the triangles similar? If so, Write a similarit statement and state the theorem or postulate that proves their similarit. If not, eplain wh not. 24 SPRING FINL REVIEW 20 C 15 1 E D 2. re the triangles similar? If so, Write a similarit statement and state the theorem or postulate that proves their similarit. If not, eplain wh not. T S U V R 3. re the triangles similar? If so, Write a similarit statement and state the theorem or postulate that proves their similarit. If not, eplain wh not. L K 5 M N P 4. re the triangles similar? If so, Write a similarit statement and state the theorem or postulate that proves their similarit. If not, eplain wh not. G 4 H 3 I E 5. re the triangles similar? If so, Write a similarit statement and state the theorem or postulate that proves their similarit. If not, eplain wh not. E V M. = Solve for k = Solve for k. k 2k

2 . = Solve for p = Solve for p p = Find the eact value of = Find the eact value of = = Find the eact value of and = = Find the eact value of and. 4ξ = = Find the eact value of and = Find the approimate length of C 1. = Find the approimate value of

3 17. θ = Find theta in degrees. θ C 1. θ = Find theta in degrees. Round our answer to the nearest hundredth θ = = Find the eact length of = Find the eact length of = Find the eact length of C = = In a given circle, the diameter is cm. Find the eact circumference and area of the circle. 23. rea = Find the approimate area of the white region. cm O 24. rea = Find the eact area of the shaded region. 4

4 25. XZ = ZY is tangent to circle X. YXZ = 0, YZ = 3. Find the length of Y XZ. Z X 2. P = Find the perimeter of the quadrilateral myz = Given that XZ is a diameter, find YZ. X (4 +21) P Y Z (3 + 40) 2. = If r = cm, find the eact length of. 135 O 29. = If r = cm, find the eact area of sector. 135 O 30. GKH = If d = 14 cm, find the approimate length of GKH. G K 5 O H 31. = If d = 14 cm, find the approimate area of sector GKH. G K 5 O H

5 32. n = circle with a radius of 3 cm has an arc length of cm. Find the measure of the arc in degrees. 33. n = circle with a radius of 2 cm has a sector area of 25 cm 2. Find the measure of the arc in degrees. 34. m 1 = Find the measure of = Find the value of. (2 + 7) (3 + 3) 3. m 1 = Find the measure of m 1 = Find the measure of m 1 = Find the measure of m 1 = Find the measure of

6 40. = Find the value of = Find the value of = Find the value of = Find the value of. in. in. 44. Write the equation of a circle centered at the origin with a radius of Write the equation of a circle centered at (3, -5) with a radius of Write the equation of a circle with a radius of and a point on the circle at (-2, 7). 47. Write the equation of a circle with diameter endpoints (-2, 7) and (, 9).

7 4. = Find the approimate area of the rectangle. Round our answer to the nearest hundredth. 2 cm 10 cm 49. = Find the eact area of the square: ξ2 in. 50. = Find the eact area of the polgon: 10 m = The diagonals of a rhombus are cm and 10 cm long. Find the area of the rhombus. 52. = Find the area of a trapezoid that is 10 in tall, and has bases of in and 12 in. 53. = Find the eact area of the regular polgon with the given side length and apothem = ξ3. 12 ft 54. S = 2 V =

8 55. S = Find the surface area and volume of a cube with a base edge of 3 cm. V= 5. S = Find the surface area and volume of the right triangular prism. V= S = Find the surface area and volume of the triangular prism. V= S = Find the surface area and volume of a regular heagonal prism that has a base edge of 10 cm, apothem = 5ξ3 and a height 1 cm. V= 59. S = Find the Surface rea and Volume of the square pramid. d V= 12 d 12 d 0. S = V = 1. S = V = Find the surface area and volume of the right cone. Find the surface area and volume of the clinder. 7 m 25 m 3 cm 4 cm

9 2. r = The volume of a right circular cone is 72 cubic centimeters, and its height is 2 cm. Find the length of the radius. 3. S = Find the surface area and volume of a sphere with diameter = 24 m. V = 4. E = If a polhedron has 11 faces and 11 vertices, which is the correct number of edges? 5. V = If a polhedron has 13 faces and 33 edges, which is the correct number of vertices?. S = V = Find the Surface rea and Volume. Slant height = 5 ft ft ft ft 7. Draw the crosssections as their two-dimensional shapes.

10 . For two independent events, P() = 0.3 and P() = 0.9. What is P( )? Let R represent the students at Hogwarts who are in the Ravenclaw house and Q represent the students who pla quidditch. 9. What is the probabilit that a Ravenclaw plas quidditch? re these events independent? Eplain The table represents some of the results of a surve of eleventh graders and twelfth graders about their preference for themes for the winter dance. Fire and Ice Eleventh Graders Twelfth Graders 75 1 Total Roaring Twenties 71. What is the probabilit that a student likes the Fire and Ice Theme given the are an eleventh grader? 72. What is the probabilit that a student likes the Fire and Ice Theme? 73. What is the probabilit that a student likes the Roaring Twenties or is a twelfth grader? 74. What is the probabilit that a student does not like the Roaring Twenties given the are in twelfth grade? 75. What is the probabilit that a student likes the Fire and Ice Theme and the are in eleventh grade?

11 7. How man distinct was can students line up for a photo? 77. How man was can ou arrange 5 students from a class of 30? 7. How man different was can ou choose a team of kids out of 20? 79. There are 7 singers competing at a talent show. In how man different was can the singers appear? 0. There are 7 singers competing at a talent show. In how man different was can the singers win first, second, and third place? 1. P(D M) = 2. P(D M) = Some of the 20 students on a prom committee are working on decorations, and some are working on music selections. Let D be the set of students working on decorations, and let M be the set of students working on music selections. 3. P(D M) C = 4. P(D) C = 5. P(M) C = 4. P(D M) =. re these events independent? Show our work. 5. P(M D) =. P(M D C ) = 7. P(M C D) =