Geometry EOC Review 2015 Geometry EOC: Power Standards by each question MULTIPLE CHOICE: #1. I can solve problems involving points, lines, planes and

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1 Geometry EOC: Power Standards by each question MULTIPLE CHOICE: #1. I can solve problems involving points, lines, planes and segments. #2. I can identify and solve problems involving special angle pairs. #3. I can read and write proofs about points, lines, segments, and angles. #4. I can identify and solve problems involving special angle pairs. #5. I can identify and solve problems involving special angle pairs. #6. I can identify and write logic statements. (conditionals versus converses) #7. I can identify and solve problems involving special angle pairs. #8. I can identify and classify types of triangles. #9. I can determine the measure of central and inscribed angles and their intercepted arcs. #10. I can use reasoning skills to make conjectures and decisions and arrive at conclusions in the form of proofs. #11. I can identify and classify types of triangles. I can solve problems involving triangles. I can read and write proofs about triangles. #12. I can identify and solve problems involving parallel and perpendicular lines. I can identify and solve problems involving special angle pairs. #13. I can solve problems involving points, lines, planes and segments. #14. I can identify and solve problems involving special angle pairs. #15. I can identify and solve problems involving special angle pairs. #16. I can identify and solve problems involving special angle pairs. #17. I can solve problems involving points, lines, planes and segments. I can identify and solve problems involving parallel and perpendicular lines. #18. I can identify and solve problems involving special angle pairs. #19. I can identify and solve problems involving parallel and perpendicular lines. I can identify and solve problems involving special angle pairs. #20. I can use the geometric mean to solve a variety of problems. I can solve problems involving triangles. #21. I can find and use perimeter and the area of plane figures to solve problems. #22. I can classify polygons based on their number of sides. #23. I can use the Pythagorean theorem to solve problems. #24. I can solve problems involving triangles. #25. I can find and use perimeter and the area of plane figures to solve problems. I can solve problems involving triangles. #26. I can determine the measure of central and inscribed angles and their intercepted arcs. #27. I can determine the measure of central and inscribed angles and their intercepted arcs. #28. I can identify and solve problems about similar figures. #29. I can use the geometric mean to solve a variety of problems. #30. I can identify and solve problems between areas of congruent & similar figures. #31. I can identify and draw transformations and use their properties to solve problems. #32. I can find and use perimeter and the area of plane figures to solve problems. #33. I can write equations for lines. #34. I can find and use perimeter and the area of plane figures to solve problems. #35. I can determine the measure of central and inscribed angles and their intercepted arcs. 1

2 #36. I can read and write coordinate proofs about quadrilaterals. #37. I can write equations for lines. #38. I can write equations for lines. #39. I can write equations for circles. #40. I can write equations for lines. #41. I can use the distance and midpoint formulas to solve problems. #42. I can apply and use properties of special right triangles to find side lengths. #43. I can find and use trigonometric ratios to find side lengths and angle measures. #44. I can find and use trigonometric ratios to find side lengths and angle measures. #45. I can find and use trigonometric ratios to find side lengths and angle measures. #46. I can determine the effects of transformations on figures on the coordinate plane. #47. I can find and use trigonometric ratios to find side lengths and angle measures. #48. I can solve problems with special quadrilaterals. I can find and use perimeter and the area of plane figures to solve problems. I can solve problems involving triangles. I can use the Pythagorean theorem to solve problems. #49. I can solve problems with special quadrilaterals. #50. I can identify and solve problems between volumes of congruent & similar figures. 2 FREE RESPONSE TOPICS: I can find and use trigonometric ratios to find side lengths and angle measures. I can apply and use properties of special right triangles to find side lengths. I can use geometric probability to solve problems. I can find the lateral area, surface area and volume of solids. I can solve problems involving triangles. I can identify and solve problems involving special angle pairs. I can write equations for lines. I can identify and draw transformations and use their properties to solve problems. I can determine the effects of transformations on figures on the coordinate plane.

3 Geometry FINAL EXAM Review I can solve problems involving points, lines, planes and segments. #1. For the next THREE questions, refer to the figure. a. Name a segment parallel to segment WY. 3 b. Name a plane that is parallel to plane ZYW. c. Name the intersection of planes VUY and ZYW. #2. A 64 foot rope is cut into 4 pieces to the ratio of 1:2:2:3. What is the length, in feet, of the longest piece? I can identify and solve problems involving special angle pairs. #1. In the figure shown, <AED is a right angle, m<aec = 58 degrees, and m<bed = 72 degrees. What is m<bec? Find x. #2 #3.

4 4 I can identify and solve problems about congruent figures (triangles). What congruence statements can be used most directly to prove the following pairs of triangles are congruent? #1. #2. #3. #4. I can use the Pythagorean theorem to solve problems. I can find and use perimeter and the area of plane figures to solve problems. #1. In this figure, what is AD, in centimeters? #2. Charles is landscaping a triangular area in her backyard. To the nearest foot, how much fencing will Charles need to enclose the area?

5 #3. A city wishes to build a new street. Two existing streets are perpendicular to one another. The new street is to begin 7 miles NORTH from the intersection point and will connect to a point on the other street that is 3 miles WEST away from the intersection point. How long will the new street be in linear miles and linear feet? If it costs $90 per linear foot to construct the new street, how much will it cost the city? REMEMBER: 1 mile = 5280 feet 5 I can identify and solve problems about similar figures #1. A 5 ½ foot tall person is standing 15 feet away from a lamppost. The light on the lamppost is 22 feet above the ground. How long, in feet, is the person s shadow? I can use the geometric mean to solve a variety of problems. #1. In right triangle DAB, segment AC is an altitude. What is AC, in centimeters? GIVEN: DC = 4; BC = 14

6 I can identify and draw transformations and use their properties to solve problems. I can determine the effects of transformations on figures on the coordinate plane. Which of the following transformations is an isometry? (An isometry is a transformation of an object in which the original object and its image are congruent.) DILATION REFLECTION ROTATION TRANSLATION 6 I can determine the measure of central and inscribed angles and their intercepted arcs. #1. Circle O has a radius of 10 cm and <ABC = 70 degrees a. What is the measure, in degrees of arc AC? b. What is the measure of <ADC? I can find and use perimeter and the area of plane figures to solve problems. #1. Find the perimeter of this triangle: I can read and write coordinate proofs about quadrilaterals. #1. The vertices of a parallelogram have coordinates as shown in this figure. What are the coordinates of B?

7 I can write equations for lines. 7 #1. What is the slope of a vertical line? #2. What is the slope of a horizontal line? #3. What is the slope of an equation of a line that is perpendicular to? y = 5 x #4. Rewrite the equation in #3 in standard form. Rewrite your answer to #3 in standard form, as well. Consider the following equation: -5x + 9y = 18 #5. Write the following equation in slope intercept form. #6. Write the equation in slope intercept form for a line that is parallel to the line above with an intercept of -17. #7. Write the equation in slope intercept form for a line that is perpendicular to the line above with an intercept of 12. Write an equation in slope intercept form for the line that satisfies the given conditions: #8. Contains the point (0, -4) and has slope -3/8. #9. m = 0 and y-intercept is -7. #10. X intercept is -2 and y-intercept is 8.

8 Use the graph to answer the following: #11. Find the slope of line p; write an equation of this line in slope intercept form. 8 #12. Find the slope of line q; write an equation of this line in slope intercept form. #13. Find the slope of a line parallel to line q #14. Find the slope of a line perpendicular to line p. I can identify and solve problems involving parallel and perpendicular lines. For the next THREE question, name the transversal AND identify each pair of angles as alternate interior, alternate exterior, corresponding, or same side interior angles. Use the figure to the right. #1. <2 and <12 #2. <3 and <5 #3. <7 and <15 #4. Use the figure shown to complete the following: Given m n and m<8 = 86, find m<13. #5. If m<3 = 4x 8 and m<9 = 2x + 26, find x. #6. If m<7 = 5x + 7 and m<14 = 5x + 3, find x. I can write equations for circles. #1. What is the center of the circle with the equation: (x + 8) 2 + (y 15) 2 = 121?

9 I can find and use trigonometric ratios to find side lengths and angle measures. #1. A rainstorm causes a tree to be broken. The top of the tree touches the ground 17 feet from the trunk of the tree and makes and angle of elevation 27 degrees with the ground. Find the ORIGINAL HEIGHT of the tree to the nearest tenth. 9 #2. A ski slope has an angle of depression of 10.8 degrees and is 256 meters long. Find the vertical drop of the slope to the nearest hundredth. #3. In ΔABC, m<a = 70, m<c = 62, and BC = 7.3. To the nearest tenth, what is AB?

10 I can identify and solve problems between volumes of congruent & similar figures. #1. TWO solids are similar with a scale factor of 4:5. a. Find the ratio of the surface areas of the two solids. 10 b. Find the ratio of the volumes of the two solids. I can use geometric probability to solve problems. #2. A circular swimming pool has diameter 60 feet and is centered in a fenced-in square region measuring 90 feet. A concrete sidewalk 7 feet wide encircles the pool, and the rest of the region is grass. a. Find the area of the water. b. Find the area of the sidewalk. c. Find the area of the grass. d. Find the volume of the pool, if the pool is 5 feet deep. e. Suppose a beach ball is thrown from the outside of the fenced in area. What is the PROBABILITY that the beach ball lands in the grassed area, assuming that lands somewhere inside the fenced in area?

11 I can apply and use properties of special right triangles to find side lengths. #1. In the figure, ΔTYZ and ΔYWZ are right triangles. Triangle ΔXYZ is an isosceles triangles with m<yxz = 120 degrees and YZ = 18 cm. Find the lengths of TY and WZ in simplest radical form with rational denominators. Show your work. 11 I can determine the measure of central and inscribed angles and their intercepted arcs.

12 I can identify and draw transformations and use their properties to solve problems. I can determine the effects of transformations on figures on the coordinate plane. 12

13 13

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