~ QRS, find the perimeter P and area A of QRS. Review Chapter 7: Similarity

Transcription

1 Review Chapter 7: Similarity 1. Find the slope of the line through the points (-6, 4) and (6, -).. x 4 0 Solve the proportion: 5 x 4. The ratio of the side lengths of a triangle is 5 : 7 :, and its perimeter is 11 ft. What is the length of the longest side? 4. Given that 8h=4k, find the ratio of h to k in simplest form. 5. DEF ~ CBA, solve for y. 6. True or false? Two equiangular triangles are similar? Why? 7. Verify that the triangles are similar. a. b. 8. Solve for x. 10. Solve for PS and SR 9. Verify that DB AE 11. Given that LMN ~ QRS, find the perimeter P and area A of QRS.

2 Review Chapter 8: Right Triangles and Trigonometry 1. Find the geometric mean of 8 and 9. If necessary, leave answer in simplest radical form.. Find the geometric mean of 14 and 1. If necessary, leave answer in simplest radical form.. Solve for x, y, and z. If necessary, leave answer in simplest radical form. 4. To estimate the height of a Douglas fir, Amy positions herself so that her lines of sight to the top and bottom of the tree form a 90 angle. Her eyes are about 1.6m above the ground, and she is standing 7.8m from the tree. What is the height of the tree to the nearest tenth of a meter? For 5 8, use the diagram on the right. 5. If PS=6 and PT=9, solve for PR. 6. Write a similarity statement comparing the three triangles. 7. If TP=4, PR=6, solve for RS. 8. Complete the equation: ST TP PR? 9. Solve for BC. Round to the nearest thousandth. 10. Solve for QR. Round to the nearest thousandth. 11. Solve for FD. Round to the nearest thousandth.

3 Use special right triangles to complete 1 0. Draw a diagram for each. Leave as a simplified radical. 1. sin0 1. sin cos sin tan sin tan sin0 cos sin 45 cos Find the value of x. Then find the value of AB, BC, and AC. Round each measure to the nearest unit.. What is the distance between: 8,10 and,0? If necessary, leave as a simplified radical.. Find the unknown measures. Round lengths to nearest hundredth, and angle measures to the nearest degree. 4. Find the unknown measures. Round lengths to nearest hundredth, and angle measures to the nearest degree. 5. An ice climber stands at the edge of a crevasse that is 115ft wide. The angle of depression from the edge where she stands to the bottom of the opposite side is 5. How deep is the crevasse at the point? Round to the nearest foot. 6. An observer in a lighthouse is 69 foot above the water. He sights two boats in the water directly in front of him. The angle of depression to the nearest boat is 48. The angle of depression to the other boat is. What is the distance between the two boats? Round to the nearest tenth of a foot.

4 For 7-0, round lengths to the nearest thousandth, and angle measures to the nearest degree. 7. Find FG. 8. Find m Q. 9. Find XZ. 0. Find m T.

5 Chapter 9 Review 1.) Find the area of the parallelogram..) Find the height of a rectangle in which w in and A 6x 4x 6 in..) Find the perimeter of a rectangle in which the width is 1 cm and the A x 4.) Find the area of a trapezoid in which b1 8 in; b 5 in; and h 6. x in. h 5x cm and A 15 x cm. 5.) Find the base of the triangle, in which 6.) Find b of the trapezoid, in which b1 mm; h 11 mm; A 1 mm. 7.) Find the area of the rhombus, in which d1 8x 7 cm; d 14x 6 cm. 8.) Find the area of the kite by first solving for x and y cm. 9.) Find the height of a parallelogram if the sides are (11.5x) mm and (0x) mm, and the Area is 18x mm. 10.) Find the perimeter of a rectangle in which w=1 cm and A x 11.) Find the base of a triangle in which h 8 cm and A 1x 8 cm. 1.) Find the area of K in terms of, if the diameter is 6 in. 1.) Find the circumference of M 5 x ft. if the area is 14.) Find the area of a regular heptagon with side length ft. 15.) Find the area of a regular nonagon with side length 8 cm. 16.) Find the area of a regular octagon with an apothem length of 4 in. 17.) Find the area of the circle not including the inscribed trapezoid. cm.

6 18.) The base and height of a rectangle are both doubled. What effect does this have on the perimeter? What about the area? 19.) The radius of a circle is multiplied by 1. What effect does this have on the circumference and the area? 5 0.) Find the probability that a point chosen randomly inside the rectangle is in the triangle. The base of the triangle is 6 in. 1.) Use the spinner below to find the probability of the pointer landing in the following areas. a. 110 b. 70 or 85

7 Chapter 10 Review 1.) What is the length of the diagonal of a cube with a side length of 1 cm? If necessary, leave as a simplified radical..) What is the height of a rectangular prism with a 0 cm by 1 cm base and a 0 cm diagonal? If necessary, leave as a simplified radical..) Find the lateral area and surface area of a rectangular prism with a base that is 9 ft by 7 ft, and a height of 14 ft. 4.) Find the lateral area and surface area of a right triangular prism with height 40 cm and base edges of 16 cm. 5.) Find the lateral area and surface area of a cube with side length 10 cm. 6.) Find the lateral area and surface area of a cylinder with a diameter of 18in and a height of 10in, If necessary, leave answer in terms of. 7.) Find the lateral area and surface area of a cylinder with a circumference of 4 cm and a height equal to half the radius. If necessary, leave answer in terms of. 8.) Find the lateral area and surface area of a hexagonal prism with height 0 in and base edge length 1 in. If necessary, leave as a simplified radical. 9.) Find the lateral area and surface area of a heptagonal prism with height 6 in and base edge length 1 in. If necessary, round to the thousandth. 10.) Find the lateral area and surface area of a regular square pyramid with base edge length 14 cm and a slant height of 6 cm. 11.) Find the lateral area and surface area of a hexagonal pyramid with a slant height of 16 in, and a base edge length of 10 in. If necessary, leave answer as a simplified radical. 1.) Find the lateral area and surface area of a right cone with radius 1 cm and a slant height of 5 cm. Leave answer in terms of. 1.) Find the lateral area and surface area of a right cone with radius 8 m and a height of 15 m. Leave answers in terms of. 14.) Find the volume of a cube with edge length 15 in. 15.) Find the volume of a right regular hexagonal prism with height of 1 in and base edge length of 9 in. Leave answer as a simplified radical. 16.) Find the volume of an oblique cylinder with a diameter of 8 in and a height of 14 in. Leave answer in terms of. 17.) Find the volume of a cylinder with base area answer in terms of. 11 cm and a height equal to twice the radius. Leave 18.) Find the volume of a rectangular pyramid with length 11 m, width 18 m, and height m. 19.) Find the volume of a square pyramid with a base edge length 9 cm and a height of 19 cm.

8 0.) Find the volume of a regular hexagonal pyramid with height equal to the apothem of the base and base edge length of 1 ft. Leave answer as a simplified radical. 1.) Find the volume of a cone with base circumference 5 in and a height in more than twice the radius. Leave answer in terms of..) Find the volume of a sphere if the diameter of the great circle is 4 in. Leave answer in terms of..) Find the diameter of a sphere with volume 6,000 cm. 4.) Find the volume of a hemisphere with radius 15 m. Leave answer in terms of. 5.) Find the surface area of a sphere with a diameter of 76 cm. Leave answer in terms of. 6.) Find the volume of a sphere with a surface area of 4. Leave answer in terms of. 7.) Find the surface area of a sphere with a great circle that has an area of 49 mi. Leave answer in terms of. 8.) Find the volume and surface area of a hemisphere with radius cm. Leave answer in terms of.

9 Chapter 11: Final Review Any measurements not labeled are in meters. 1. FE and FG are tangents to the circle. Find FG.. Find m DCA.. AB CD. AB 9n 11 cm and CD 7n 11 cm. Find CD. 4. C J, DG 14x 6, MN 5x 1, and mgcd mnjm. Find NM. 5. T U, and AC 47.. Find PL to the nearest thousandth.

10 6. Find the area of sector LKM. Leave answer in terms of. 7. Find the area of sector AKL. Leave answer in terms of. 8. Find the area of segment formed by the two radii and chord. Leave answer in terms of. 9. Find m LAK m LAK x m LDK x when 5 7 and. 10. Find each measure if macf 11 and mab 145. a.) m DAB b.) meca c.) mbc d.) m DAC e.) m BAC f.) mac

11 11. Find the maed, if mbc 11 and mad Solve for myz. 1. Find the value of x. 16. Solve for x. 1. Find the value of x. 17. Solve for x. 14. Find myz. 18. Solve for x.

12 Unit 0: Final Review Convert the following into scientific notation. 1.),10,000.) ) ) 5.) 6.) Convert the following into standard form. 7.) ) Order the following from greatest to least. Remember to write the order with the original numbers. 9.) , , , 1.610, ) , 5.110, , , Solve the following problems by writing an expression, showing all work, and writing your answer in a complete sentence in the specified notation. 11.) If sound travels miles in one hour. How many miles will it travel in 1 minute? Write your answer in scientific notation. 1.) A speck of dust in an electron microscope is millimeters wide. The image is 5 10 times larger than the actual size. How many millimeters wide is the actual speck of dust? Write your answer in standard notation. 7 1.) The state of Connecticut covers 6 10 square miles. The Indian Ocean covers about square miles. How many times bigger than Connecitcut is the Indian Ocean? Write your answer in scientific notation ) The population of the United States is.5 10 and the population of the world is How many times larger is the population of the world than the US? Write your answer in scientific notation. Convert the following fractions, decimals, and percents into the values that are not already given. For example, if a fraction is given, you must convert into the decimal and percent equivalencies. All fractions must be simplified. Show all work. Circle your final answers! (4 pts each) ) 0.) ) 16.) ) 8.% 18.) ) 8.5%.) ) ).89 Simplify. Leave your answer in exponential notation with positive exponents and if possible one base. Show all work ) ) 6.) ) ) ) 1.)

13 81.) 1.) 7x 6 9x ) 4x 4.) 8m 4 9 n 1 6 m n 5.) x y 5 7.) Write down all the expressions below that are equal to 9. To earn full credit, work or an explanation must be shown for each expression as proof as to why you did or did not circle it