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Spring Final REVIEW
Spring Final REVIEW Name:_____________________________ Chapter 7 2. Consecutive angles in a parallelogram are always ____________. 1. State which theorem you can use to show that the quadrilateral is a parallelogram. a) Parallelogram Opposite Angles Converse b) Parallelogram Opposite Sides Converse a) Congruent Angles b) Complementary Angles c) Supplementary Angles d) Vertical Angles c) Parallelogram Diagonals Converse d) Opposite sides Parallel and Congruent Theorem 3. If 𝑂𝑁 = 6𝑥 − 6, 𝐿𝑀 = 5𝑥 + 2, 𝑁𝑀 = 𝑥 + 5, and 𝑂𝐿 = 3𝑦 + 7, find the values of 𝑥 and 𝑦 given that LMNO is a parallelogram. 4. Find the value of x. 5. Find the value of x. 6. Classify the special quadrilateral. 7. Classify the special quadrilateral. Spring Final REVIEW Name:_____________________________ Chapter 8 8. Tell whether the triangles are similar. 10. Given that ∆𝐴𝐵𝐶 ~∆𝐷𝐸𝐹, solve for 𝑥 and 𝑦. 9. Find the length of ̅̅̅̅ 𝐴𝐵. 11. The perimeter of ∆𝑃𝑄𝑅 is 56, 𝑃𝑄 = 16, ∆𝑃𝑄𝑅 ~∆𝑆𝑇𝑈, 𝑆𝑇 = 12. What is the perimeter of ∆𝑆𝑇𝑈? 13. ∆𝐴𝐵𝐶 ~ ∆𝑅𝑆𝑇, find the value of 𝑥. 12. Shown below is an illustration of the ____________. a) AA Similarity b) SAS Congruence c) SSS Similarity d) SAS Similarity 14. A rectangular yard is fenced using 319 feet of custom fence. Your friends really like the fence and decide to fence in their yard using the same fence. Their yard is similar but has a scale factor 8 of 5 times the size of yours, how much fence, to the nearest foot, will they have to purchase? 15. ∆𝐴𝐵𝐸 ~ ∆𝐶𝐷𝐸. Find the length of altitude ̅̅̅̅ 𝑁𝐸 . Spring Final REVIEW Name:_____________________________ Chapter 9 16. Find the value of 𝑥 and 𝑦. Write your answer in simplest form. 17. Find the value of 𝑥 and 𝑦. Write your answer in simplest form. 19. Find the length of the hypotenuse of the triangle. 21. Find the value of x. Write your answer in answer in simplest form. 18. Find the value of 𝑥. 20. Find the value of 𝑥. Write your answer in simplest form. 22. You are holding a kite in your hand. The angle of elevation from your hand to the kite is 40° and the distance to the kite is 295 feet. Your hand is 4 feet above ground. How high is the kite? Round your answer to the nearest tenth of a foot. 24.Find the 𝑚 < 𝐻and 𝑚 < 𝐺. 23. Find 𝑤. 25. An adventure company wants to run a zip line from the top of one building that is 130 feet tall to the top of another building that is 30 feet tall. The two buildings are 72 feet apart. Estimate the length (in feet) of the zip line. Round your answers to the nearest tenth. Spring Final REVIEW Name:_____________________________ Chapter 10 ̂ = 105° and 𝑟 = 10 yards. 26. In circle 𝑃, 𝑚𝐴𝐵 ̂ . Round your answers to Find arc length of 𝐴𝐵 two decimal places. 27. Find the value of 𝑥. 28. Write the standard equation of a circle that has center of (−4, −2) and a radius of 8. 29. Write the standard equation of a circle that has center of (8, 1) and a radius of 5. 30. Name a radius, chord, diameter, secant and a tangent. 31. In the diagram, 𝑄𝑅 = 𝑆𝑇 = 144, 𝐶𝑈 = 3𝑥, and 𝐶𝑉 = 6𝑥 − 21. Find the value of 𝑥. 33. Find the value of 𝑥. 32. In the diagram, 𝑚 < 𝐽 = 39.5°. ̂. Find the 𝑚𝐽𝐾 Spring Final REVIEW Name:_____________________________ Chapter 11 34. Convert 2𝜋 3 ̂ . Round your 36. Find the arc length of 𝐹𝐸 answer to two decimal places. radians to degrees. 𝜋 35. Convert 6 radians to degrees. 37. Find the area of the regular polygon. Round your answers to two decimal places, if necessary. 38. Find the area of the composite figure. Round your answer to two decimal places, if necessary. 39. Wallpaper is applied to the wall surrounding a Norman window. How many square feet of wallpaper are required to cover the wall surrounding the window? 40. About 78,000 people live in one-fourth of a region with a 15 mile radius. Estimate the population density in people per square mile. 41. All linear dimensions of a regular polygon are 1 multiplied by 4. Describe the area, in square units, of the new polygon? 42. A water wheel has a radius measuring between 13 feet and 24 feet. The wheel is about to turn 7𝜋 9 radians from its starting position before getting stuck. Which distances could the wheel spin before it would no longer be about to move? a) 31.76 ft c) 56.20 ft b) 61.09 ft d) 63.53 ft 43. The diameter of ⨀𝑄 is 14 cm. Find the arc ̂. length of 𝑃𝑅 Spring Final REVIEW Name:_____________________________ Chapter 12 Describe the cross section formed by the intersection of the plane and the solid. 44. 45. 47. Find the volume, lateral area, and surface area of the cylinder. 49. The volume of a right cylinder is 300𝜋 cubic feet. The dimension of the radius is doubled and the height remains the same to create a new right circular cylinder. What is the volume of the new right circular cylinder? 51. Find the volume, lateral area and surface area of the rectangular prism. 46. 48. Find the volume and surface area composite solid. 50. Describe how tripling all linear dimensions affects the volume of the cylinder. 52. Find the volume and surface area of the composite solid.