Geometry EOC. SOL Simulation

Transcription

1 Geometry EO SOL Simulation Graphing alculator ctive hesterfield ounty Public Schools epartment of Mathematics

2 1 George used a decorative gate to connect the fencing around his backyard. E F 60 G 120 Using the information on the diagram and assuming the top and bottom are parallel, m is 40º 60º 120º 180º 2 Which is the biconditional of the following statement? If a polygon is a triangle, then it has exactly three sides. polygon is not a triangle if and only if it does not have three sides. polygon is a triangle if and only if it has exactly three sides. If a polygon has exactly three sides, then it is a triangle. If a polygon does not have exactly three sides, then it is not a triangle. Geometry EO SOL Simulation Page 1 of 29 hesterfield ounty Public Schools

3 3 Given: p q, m n, and m 1 = q 2 p m n What is m 2? 15º 75º 105º _ 165º 4 Given: angle What is the first step in constructing the angle bisector of angle? raw. raw a line segment connecting points and. From points and, draw equal arcs that intersect at. From point, draw an arc that intersects each side of the angle. Geometry EO SOL Simulation Page 2 of 29 hesterfield ounty Public Schools

4 5 In the diagram, ' ' ' is a transformation of, and " " " is a transformation of ' ' '. y x The composite transformation of of a to is an example reflection followed by a rotation. reflection followed by a translation. translation followed by a rotation. translation followed by a reflection. 6 etermine which statement best represents the information in the figure. E F E F and E F EF and E F EF and F F E F and EF Geometry EO SOL Simulation Page 3 of 29 hesterfield ounty Public Schools

5 7 Which conclusion logically follows the true statements? If the football team doesn t score, they will lose the game. If the football team loses the game, they will not play for the championship. If the football team wins, they will not play for the championship. If the football team scores, they will play for the championship. If the football team doesn t score, they will play for the championship. If the football team doesn t score, they will not play for the championship. Geometry EO SOL Simulation Page 4 of 29 hesterfield ounty Public Schools

6 8 Given: k p k 5 6 p Which of the following is NOT a valid proof that m 1 + m 6 = 180? Statements Reasons 1. k p 1. Given 2. 1 = m 5 m 2. If two parallel lines are cut by a transversal, corresponding angles are congruent 3. m 5 + m 6 = efinition of linear pair 4. m 1 + m 6 = Substitution property Statements Reasons 1. k p 1. Given 2. 1 = m m 6 = 180 m 2. efinition of vertical angles. m 3. If two parallel lines are cut by a transversal, same side interior angles are supplementary 4. m 1 + m 6 = Substitution property Statements Reasons 1. k p 1. Given m 2 = 180 m 2. If two parallel lines are cut by a transversal, alternate exterior angles are supplementary 3. m 2 = m 6 3. If two parallel lines are cut by a transversal, corresponding angles are congruent 4. m 1 + m 6 = Substitution property Statements Reasons 1. k p 1. Given 2. m 1 + m 3 = efinition of linear pair If m two 3 = lines m 6 are parallel, 3. corresponding If two parallel angles lines are are cut congruent. by a 3. Vertical angles are congruent. transversal, alternate interior angles are congruent 4. m 1 + m 6 = Substitution property Geometry EO SOL Simulation Page 5 of 29 hesterfield ounty Public Schools

7 9 Which geometric construction is shown in the diagram? a line segment congruent to a given line segment. a line parallel to a given line a perpendicular bisector of a segment a bisector of a given angle 10 Quadrilateral has vertices (-2, 2), (4, 5), (3, 0) and (-3,-3). What are the coordinates of the midpoint of diagonal? 1, 1 2 1, , 2 (1, 1) Geometry EO SOL Simulation Page 6 of 29 hesterfield ounty Public Schools

8 11 If p q, what is the measure of? ( 5x + 14) p ( 19x 28) q t 1 12 The equation of line k is y = x 2. 3 The equation of line m is 2 x + 6 y = 18. Lines k and m are parallel perpendicular the same line intersecting but not perpendicular Geometry EO SOL Simulation Page 7 of 29 hesterfield ounty Public Schools

9 13 Given: LM and QR are parallel Given: m M = m L = 50. M R L N P Q What is 130º 100º _ 80º 50º m QNP? Geometry EO SOL Simulation Page 8 of 29 hesterfield ounty Public Schools

10 14 Scott is constructing a line perpendicular to line l from point P. Which of the following should be his first step? _ Geometry EO SOL Simulation Page 9 of 29 hesterfield ounty Public Schools

11 15 Students fter School ctivities lubs Sports Music ased strictly on this diagram representing students participating in after school activities, which statement represents the shaded region? Some students participate in sports and music, but not clubs. Some students participate in clubs and music, but not sports. Some students participate in sports, music, and clubs. ll students participate in sports and music. 16 If triangle XYZ is reflected across the x-axis to form triangle X 'Y 'Z', what are the coordinates of Z'? (2, -3) (2, 3) (-2, 3) (3, 2) Geometry EO SOL Simulation Page 10 of 29 hesterfield ounty Public Schools

12 17 onsider the following statements represented by p and q : p: The sum of two angles is 180. q: The two angles are supplements. Which of the following is a symbolic representation of the statement If two angles are not supplements, then the sum of the two angles is not 180. q p _ p q ~q ~ p ~p ~ q 18 This figure has point symmetry only line symmetry only_ point and line symmetry neither point nor line symmetry Geometry EO SOL Simulation Page 11 of 29 hesterfield ounty Public Schools

13 19 QJK ~ QRS. Which of the following statements is NOT true? QJ QK = QR QS JK QK = RS QS QR QS = JK RJ QR = QS QJ QK Geometry EO SOL Simulation Page 12 of 29 hesterfield ounty Public Schools

14 In the following diagram, it is given that is the midpoint of, that, and that E. E Prove E by selecting the most logical sequence of statements and reasons. Statements Reasons 1. is a midpoint of 1. Given efinition of Midpoint 3. E 3. Vertical angles are congruent 4. and E 4. Given 5. and E are right angles E E Perpendicular lines form four right angles 6. ll right angles are congruent 7. ngle-side-ngle (S) 5. Given 6. ll right angles are congruent 7. ngle-side-ngle (S) 5. efinition of congruent angles 6. ll right angles are congruent 7. Side-ngle-Side (SS) 5. Perpendicular lines form four right angles 6. lternate interior angles are congruent 7. Right triangles are congruent to each other Geometry EO SOL Simulation Page 13 of 29 hesterfield ounty Public Schools

15 21 For what value of x is ~ EF? x + 3 E F Select all sets of given triangle lengths that would form a right triangle. I. 3, 4, 6 III. 11, 60, 61 V. 7, 24, 25 II. 8, 15, 17 IV. 5, 7, 12 VI. 12, 15, 18 II, IV, V II, III, V I, V, VI IV only 23 Which set of lengths could be the lengths of the sides of a triangle? 1, 2, 3 6, 6, 14 7, 24, 25 10, 20, 33 Geometry EO SOL Simulation Page 14 of 29 hesterfield ounty Public Schools

16 24 Roof trusses often use right triangles to make a flimsy 2 x 4 more rigid to hold up the weight of the roof. If a house is 40 feet wide and the roof is an isosceles triangle with base angles of 30 degrees, how far is it from the bottom edge of the roof to the peak? x feet ft ft 20 3 ft _ 40 ft 25 On a map, Richmond, anville, and harlottesville form a triangle. harlottesville is 85 miles from Richmond and anville is 100 miles from Richmond. Which is a possible distance between anville and harlottesville? 5 miles 15 miles 150 miles 185 miles Geometry EO SOL Simulation Page 15 of 29 hesterfield ounty Public Schools

17 26 In scalene triangle, m = 45 and m = 55. What is the order of the sides in length, from longest to shortest?,,,,,,,, 27 Pedro has a square practice net in his backyard. The diagonal of the net is 6 feet. Find the length of one side of the net. 3 2 feet 2 3 feet 3 feet 12 feet 28 surveyor is trying to determine the width of a river. He first stands at point, directly opposite a tree at point. He then walks 100 feet to point. He measures the acute angle at point to be 79. What is the width, w, of the river? 100 ft 79 w 19.4 feet feet feet feet Geometry EO SOL Simulation Page 16 of 29 hesterfield ounty Public Schools

18 29 From the top of a 210 foot tall lighthouse, the angle of depression to a boat is 27. Find the distance from the boat to the base of the lighthouse feet 107 feet feet feet Geometry EO SOL Simulation Page 17 of 29 hesterfield ounty Public Schools

19 30 and point E are shown in the diagram below. y E x etermine a possible location of point to make E. (2, 2) (4, 1) (3, 1) (4, 2) 31 Given quadrilateral, where,, and a diagonal. Which method can be used to prove? ngle-ngle-side (S) Side-Side-ngle (SS) Side-ngle-Side (SS) Side-Side-Side (SSS) Geometry EO SOL Simulation Page 18 of 29 hesterfield ounty Public Schools

20 32 Scott wants to swim across a river that is 400 meters wide. He begins swimming perpendicular to the shore he started from but ends up 100 meters down river from where he started because of the current. How far did he actually swim from his starting point? 300 m m m 500 m Geometry EO SOL Simulation Page 19 of 29 hesterfield ounty Public Schools

21 33 tiled floor consists of a tessellating pattern of two regular polygons. portion of the tiled floor is shown below. What two regular polygons are used in the tessellating pattern? Octagons and Squares Hexagons and Squares Pentagons and Squares ecagons and Squares Geometry EO SOL Simulation Page 20 of 29 hesterfield ounty Public Schools

22 34 In the drawing, is a parallelogram. What must be the coordinates of the intersection of the diagonals? y (a c, b) (a, b) ( c, 0) x a b, 2 2 a c b + c, 2 2 a + c b, 2 2 a c b, The exterior angle of a certain regular polygon is 60. How many sides does the polygon have? Geometry EO SOL Simulation Page 21 of 29 hesterfield ounty Public Schools

23 36 city park can be represented by trapezoid EFG, where E FG, and F and EG represent hiking paths that span the diagonals of the park. planning team is interested in planting additional trees throughout the park and has measured some of the angles between the edges of the park and the sidewalks as shown in the diagram below to determine the best location for the trees. 24 E G F Using the information in the diagram, find m FG. Geometry EO SOL Simulation Page 22 of 29 hesterfield ounty Public Schools

24 37 spotlight, located at point S in the diagram below, illuminates parts of a circular pond. Light is beamed at an angle of 25 from the spotlight and intercepts the circle such that the m = 40. S 25 Find m Rectangle QRST is shown. Q R T S Which of the following would be a reason to claim that QRST is NOT a square? QS = RT QT QR QT TS QR TS Geometry EO SOL Simulation Page 23 of 29 hesterfield ounty Public Schools

25 39 In square, = 3x 4 and E = x + 6, where E is the intersection of the diagonals. E What is the length of? is inscribed in circle O, and passes through O. 40 O If m = 40, find m Geometry EO SOL Simulation Page 24 of 29 hesterfield ounty Public Schools

26 41 circle has center (-2, 3) and radius 4 units. Which of the following is a point on the circle? (-2, 5) (-2, -1) (2, 7) (-6, 7) 42 t Greg s Greek Gourmet, diners have an opportunity to throw a dart at a dartboard to earn a discount on their meal. The dartboard is a circle with radius of 8 cm and is divided into two sectors. arts that land in the unshaded sector get a free meal, and darts that land in the shaded sector get $5 off. The dartboard is modeled by circle O below. $5 off O FREE MEL If m = 135, find the area of the dartboard that corresponds to a $5 discount. 2 6π cm 2 10π cm 2 24π cm 2 40π cm Geometry EO SOL Simulation Page 25 of 29 hesterfield ounty Public Schools

27 43 The coordinates of the endpoints of a diameter of a circle are (6, 2) and (0, -2). Which of the following is an equation of the circle? 2 2 ( x 3) + y = 13 x 2 + ( y 3) 2 = ( x 3) + y = 52 x 2 + ( y 3) 2 = In circle P, is a diameter and is perpendicular to at E. If P = 7 and E = 4, find E. E P Geometry EO SOL Simulation Page 26 of 29 hesterfield ounty Public Schools

28 45 Lea made two candles in the shape of right rectangular prisms. The first candle is 15 cm high, 8 cm long, and 8 cm wide. The second candle is 5 cm taller but has the same length and width. How much additional wax was needed to make the taller candle? cm cm cm cm 46 tepee with a dirt floor in the shape of a right cone has a slant height of 26 feet and a radius of 12.5 feet. pproximately how much canvas would be needed to cover the tepee? 3730 sq ft _ 4254 sq ft 1511 sq ft 1021 sq ft 47 The ratio between the volumes of two cubes is 125 to 216. What is the ratio between their respective surface areas? 5:6 25:36 125: :432 Geometry EO SOL Simulation Page 27 of 29 hesterfield ounty Public Schools

29 48 Which of the following would triple the volume of the Egyptian square-based Pyramid below? add 3 to each dimension of the Pyramid multiply every dimension of the Pyramid by 3 multiply only the height by 3 add 3 to the slant height 49 In circle P, T and T intersect at T. T=10, T=8, =12, and =x+2. Find. P T Geometry EO SOL Simulation Page 28 of 29 hesterfield ounty Public Schools

30 50 Which of the following three-dimensional shapes have equivalent surface areas? Figure 1 Figure 2 Figure 3 7 cm Figure 4 Figures 1 and 2 Figures 2 and 3 Figures 3 and 4 Figures 1 and 4 Geometry EO SOL Simulation Page 29 of 29 hesterfield ounty Public Schools