Geometry Core Content EOC Exam Review
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1 Geometry Core Content EOC Exam Review 1. What is the midpoint of a line segment with endpoints ( 3, 7) and (6, 5)? 2. What is the midpoint of a line segment with endpoints ( 1, -5) and (-10, 3)? 3. In your own words, state a. The Segment Addition Postulate b. The Angle Addition Postulate c. The Addition Postulate 13. Orlando is visiting Big Tree National Park. He sees that the top of a large redwood tree is at a 60 degree elevation in relation to the ground. He is standing 40 feet from the bottom of the tree. How tall is the tree? Round the answer to the nearest tenth. 4. What is the distance between the two points (-2, 6) and (4, 3)? 5. What is the distance between the two points (5, 7) and (-2, -2)? 6. A right triangle has a hypotenuse with a length of 8 inches and a leg with a length of 4 inches. What is the length of the other leg? 7. A right triangle has a hypotenuse with a length of 5 units and a leg with a length of 4 units. What is the length of the other leg? 14. A triangle on the coordinate plane has vertices located at A(1, -2), B(9, 4) and C(7, -2). Determine the area of the triangle. 8. What must be true about the equations of two lines that are parallel? Use an example to explain. 9. Given line p has the equation y = 2x +1, what is the equation of a line that is perpendicular to line p and passes through the point (0, 3)? 10. Match the example with the property: Example Property If x = 2y, and x + y = 10, then 2y + y = 10 AB = AB If x + 7 = y + 12, then x = y + 5 Addition Property Substitution Property Reflexive Property 15. Determine the area of the trapezoid. 11. Triangle ABC has points A(-3, 0), B(0, 3), and C(3, 0). Classify the triangle by sides and by angles. 12. Triangle XYZ has points X(1, 3), Y(1, 6), and Z(-4, 3). Classify the triangle by sides and by angles.
2 16. In the diagram below, the parallelogram is translated so that is at the point (0, 0). What are the coordinates for B? 22. Brandon bisects angle KMN and labels a point on the bisector as P. He measures angle KMP with a protractor. The measure of angle KMP is 32. What is the measure of angle KMN? 23. Amanda bisects angle LMT and labels a point on the bisector as R. She measures angle LMT with a protractor. The measure of angle LMT is 32. What is the measure of angle LMR? 24. A square pyramid has a volume of 144 cubic centimeters and a height of 12 centimeters. What is the length of each side of the base? 17. In the diagram above, the parallelogram is translated so that is at the point (0, 0). What are the coordinates for D? 18. Given a cone with a radius of 8 centimeters and height of the cone is 3 centimeter. What is the Volume of the cone? 25. The cylinder shown has a diameter of 12 inches. If the height of the cylinder is 9 inches, what is the Surface Area of the cylinder? 19. Given a cone with a radius of 10 centimeters and height of the cone is 4 centimeter. What is the Volume of the cone? 26. What is the length of to the nearest tenth? 20. What is the volume of the sphere shown if r = 10 inches? 27. Solve for b in the figure shown. 21. What is the volume of the sphere shown if r = 14 inches?
3 28. In the diagram shown, and AB = 25 feet. Which equation can be used to calculate the value of x? a. x = 49(sin 39 ) b. x = 49(cos 39 ) c. x = 49(tan 39 ) d. x = sss Lines m and n and p all lie in the same plane. Lines m and n are parallel. Line p is perpendicular to line m. What is the relationship between lines n and p? a. Lines n and p are parallel. b. Lines n and p are skew. c. Lines n and p are perpendicular. d. Lines n and p are the same line. 32. Which of these quadrilaterals are not parallelograms? Square Kite Rhombus Trapezoid Rectangle 33. True or False: A rhombus is never a trapezoid. Explain your reasoning. 34. What is the perimeter of the rhombus shown? 35. What is the perimeter of the kite shown? 30. In the figure shown, sinp = What is the length of? 36. If msv = 170 and mrt = 20, what is the m RQT? 31. In the isosceles triangle shown, the measure of the exterior angle HQM is 110. What is the measure of NMQ?
4 37. If mmq = 178 and mln = 58, what is the m MPQ? 41. Which of the following statements about figures associated with circles is true? A secant intersects a circle in two points. A tangent line is perpendicular to an intersecting radius. A diameter is a chord. A tangent segment is called a chord. 42. Solve for x. 38. In the diagram shown, what is the measure of the angle labelled 1? 43. Two secants intersect at a point outside the circle. Write an equation that shows the relationship between the lengths of the segments shown. Then solve for x. 39. In the diagram shown, what is the measure of the angle labelled 1? 40. In circle F, chords AC and BD intersect at point E. The lengths in feet of each segment are shown. What is the length of AE? 44. Part of a circular toy was found. It was measured to be only a 70 section of it was left. If the toy had a radius of 3 inches, what was the area of this sector of the toy?
5 45. A circle is inscribed in a square. If the radius of the circle is 20 meters, what is the area of the shaded region? 49. Use the diagram to write an equation and solve for x. 46. What is the area of the circle? 50. In the diagram shown, what is the value of x? 47. Sarai plots and connects the following points: A(0, 0), B(-5, 0), C(-7, 3) and D(3, 3). Which best describes the shape formed? a. Rectangle b. Rhombus c. Triangle d. Trapezoid e. None of the above 48. In the diagram shown, what is the value of x? 51. While hiking in the Del Norte National Forest, Dan used a mirror to sight the top of a redwood tree. He was wanted to know it s height so he measured his distance to the mirror and the tree s distance to the mirror. If Dan s eyes are 6 from the ground, how tall is the tree? 52. Which theorem or postulate can be used to prove that DEF is similar to ABC? a. Side-Side-Side Similarity Theorem b. Side-Angle-Side Similarity Theorem c. Angle-Angle Similarity Theorem d. Side-Side-Angle Similarity Theorem
6 53. Read the proof below. Complete the proof by writing the reasons for each statement. Given: Prove: 3 and 6 are supplementary. Statements Reasons and 2 are supplementary 3. m 3+ m 2 = m 3+ m 6 = and 6 are supplementary 54. In triangle ABC, what is the value of x? In the diagrams below, which pair(s) of triangles must be similar? 55. Given: XY // WZ and XY WZ Which theorem or postulate listed below could be used to prove that WXY YZW? a. AAS b. SSS c. SAS d. AAA
7 57. Which theorem or postulate listed below could be used to prove that the two triangles shown are congruent? 59. Below are the first steps in a number of classic constructions with a compass and a straight edge. Identify each construction. a. a. AAS b. SSS c. SAS d. AAA 58. Which set of congruence statements show that by the ASA Congruence Theorem? b. c. d. a. P L LN PR LM PQ c. N R NM RQ LM PQ b. L Q LN PR LM PQ d. P L N M NM RQ e.
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