Geometry Name: Q3 Exam Review Date: Per: Show all your work. Box or circle your final answer. When appropriate, write your answers in simplest radical form, as a simplified improper fraction, AND as a decimal rounded to the nearest thousandths place. REMEMBER UNITS! L15 1. Which statements below are true? (Choose all that apply.) A) You can solve a right triangle if you are given the lengths of two sides. B) You can solve a right triangle if you are given the measure of the two acute angles. C) You can solve a right triangle if you are given only one side and one actute angle. D) You can solve a right, isosceles triangle if you are given the length of one side. 2. Find the value of the variable to the nearest hundredth. Unknown units are in meters. a) θ = 8yd b) x = 49yd θ θ c) θ = 15 ft d) x = 4 12 ft y = x y y e) x = f) x = y = y = y 3 x y 30 15 m x
3. Express sin A, cos A, and tan A as ratios. Then find m A and m B. Compare the quantity in Column A with the quantity in Column B. Choose the letter that best answers the question. A) The quantity in Column A is greater. B) The quantity in Column B is greater. C) The two quantities are equal. D) The relationship cannot be determined on the basis of the information supplied. Column A Column B 4. AB BC 30 6m 45 5. Describe each angle as it relates to the objects in the diagram. 6. A building near Atlanta, Georgia, is 181 feet tall. On a particular day at noon it casts a 204-foot shadow. What is the angle of elevation from the top of the shadow to the top of the building?
7. The captain of the boat knows that the lighthouse on the coast is 100m tall. If she measures the angle of elevation to be 2, how far is the boat from the coast? 8. A hot-air balloon is competing in a race. After 20 minutes, the balloon is at an altitude of 300m. The pilot can still see the starting point at a 25 angle of depression. How many meters is the balloon from the starting point on the ground? L16 9. What quadrilaterals meet the conditions shown? The figure is not drawn to scale. 10. Name all quadrilaterals that have: Perpendicular Diagonals Congruent Diagonals Angle Bisector Diagonals 11. True or False? a) All trapezoids are quadrilaterals. b) A rectangle is a square. c) Some parallelograms are rectangles. d) A rhombus is a square.
Find the value of the variable(s). Then, find the lengths of the sides and/or the measure of the angles. 12. 13. 14. (2w) Find the angle measures in ABCD. 15. 16. (3x+6) (x+y) (4y+7) Find the angle measures of KITE. 17. 18. (16x 63) (3y+7) 152 (4x+45)
19. x = x+2 13 y = x+4 y-6 20. Find the indicated variable(s) or side length. a) b) Parallelogram WATE w = (2x+30) WT = x = 5 y = z = c) In isosceles trapezoid JKLM, MK = 3x + 1 and LJ = 2x + 7. MK = 21. Find the measure of angle A. m A = m B = m C = m D =
22. WXYZ is a quadrilateral. Which information would allow you to conclude that WXYZ is a parallelogram? Hint: Draw diagrams to help you. (Choose all that apply.) A) WX ZY & WZ XY B) W Y & X Z C) WX ZY & WZ XY D) WZ XY & WX ZY E) WZ XY & WZ XY 23. If WX = 58 in, find JL. JL = The midsegment of the trapezoid is RT. Find the value of x. 24. 25. 26. x x
L17 27. Given segment BG whose endpoints are B( 7, 1) and G( 3,11). a) Find the coordinates of the midpoint of the segment b) Find the length of the segment. Leave your answer in simplest radical form and as a decimal rounded to the nearest 3 decimal places. c) Find the slope of the segment. 28. Parallel lines have slope. Perpendicular lines have slopes. m AB = a) Find the slopes of AB and CD, where A( 7, 4), B( 3,2), C( 3,0), D( 9,4). Then, decide m CD = whether the lines are parallel, perpendicular, or neither. b) Write an equation of a line parallel to 4y = 3x 40. c) Write an equation of a line perpendicular to 2y =12x +18. Find the slope of the lines shown, and decide whether the lines are parallel, perpendicular, or neither. Explain. 29. 30. 31. 32.
33. Describe any relationship between lines q, r, s, and t. q : 6x + 8y =12 r : y = 4 3 x + 17 3 s : 6x 8y =18 t : y = 4 3 x 4 Write an equation parallel to the given line. Then, write an equation perpendicular to the given line. 34. y = 5x 35. y = 1 3 x 1 What special type of quadrilateral has the vertices given? Justify your answer. 36. P(5, 4), Q(3, -6), R(0, -10), S(2, 0) 37. L(4, 8), O(0, 9), V(-2, 1), E(2, 0) Now, for #37, write a plan to prove that the diagonals are congruent.
L21 38. Find the value of the indicated variable. x = d) x 118 108 80 112 39. 40. 41. Find the sum of the exterior angles in a nonagon. 42. Find the measure of one interior angle of a regular heptagon. Round to the nearest degree. 43. Find the number of sides in a regular polygon if an exterior angle is 120. Then classify the polygon by its number of sides.
44. The polygon to the right is best described as _?_. a) (Choose all that apply.) A) equilateral B) equiangular C) triangle D) quadrilateral E) pentagon F) hexagon b) G) heptagon H) octagon I) nonagon J) decagon K) dodecagon L) n-gon (specify) c) 45. Find the area of the given figure. a) b) c)