GEOMETRY Spring Packet. Good Luck To: Date:


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1 Good Luck To: Date: MA.912.G has an endpoint at (2, 1) and a midpoint at (8, 3). Which measure is closest to the length of? A units B. 8.9 units C units D units MA.912.G In the diagram below, the angle of depression from P to Q is 45. Which of the following is closest to the distance between P and Q? A ft. B ft. C ft. D ft. MA.912.G Five spheres are being painted for a display at a store. If the diameter of each sphere is 7 centimeters, which value is closest to the total surface area that will be painted? A. 770 B. 154 C. 192 D. 440 MA.912.G For triangles and, and. Based on this information, which statement is a reasonable conclusion? A. because they are corresponding angles of congruent triangles. B. because they are corresponding parts of congruent triangles. C. because they are corresponding angles of similar triangles. D. because they are corresponding parts of similar triangles. Page 1 of 22
2 MA.912.T On the map below, Main Street, 10th Street, and Highway 1 intersect to form a right triangle. The distance between 10th Street and Main Street along Highway 1 is 5.6 mi. Which measure is closest to the length of Main Street from Highway 1 to 10th Street? A. 8.7 mi B. 3.6 mi C. 4.7 mi D. 7.3 mi MA.912.G The side length of a smaller square is onethird the side length of a larger square. Which of the following statements describes the area of the smaller square? A. The area of the smaller square is the area of the larger square. B. The area of the smaller square is the area of the larger square. C. The area of the smaller square is the area of the larger square. D. The area of the smaller square is the area of the larger square. MA.912.G Southern Memorial Park in North Miami Beach is bounded on the west by NE 16 th Ave., on the east by NE 18th Ave., on the north by NE 157th Terrace, and on the south by NE 151st Street. All roads are straight and intersect in right angles. Diagonals across the park are congruent. What type of quadrilateral is Southern Memorial Park? A. parallelogram B. rectangle C. rhombus D. trapezoid Page 2 of 22
3 MA.912.G Rectangle STUW is shown below. What is ST? A. 33 in. B. 24 in. C. in. D. in. MA.912.G The hand on the circular clock in the figure below measures 10 cm. Which of the following is closest to the distance that the tip of the hand travels as it moves from the 12 to the 3? A. 79 cm B. 21 cm C. 63 cm D. 16 cm MA.912.G Devon and Jamal both draw regular polygons. Devon s polygon has 14 sides. Jamal s polygon has 15 sides. Which statement is NOT true? A. The measures of all the exterior angles of Devon s polygon are equal. B. The sum of all the exterior angles of Devon s polygon equals the sum of all the exterior angles of Jamal s polygon. C. The measure of one of the exterior angles of Jamal s polygon is greater than the measure of one of the exterior angles of Devon s polygon. D. The measure of one of the exterior angles of Jamal s polygon plus the measure of the adjacent interior angle is 180. Page 3 of 22
4 MA.912.G In the figure below, and. Based on this information, which statement can be proved true? A. B. CAB is an acute triangle. C. D. CAB is a right triangle. MA.912.G Susie s teacher draws the quadrilateral shown below on the board. Which of these observations cannot be used to prove that the quadrilateral is a parallelogram? A. The opposite sides are congruent. B. Both pairs of opposite angles are congruent. C. One pair of opposite sides is congruent and parallel. D. The diagonals are perpendicular. MA.912.G ΔABC has vertices at A(0, 0), B(9, 12), and C(25, 0). What is the distance between the midpoint of AB and the midpoint of AC? A. 7.5 units B. 10 units C. 15 units D. 20 units Page 4 of 22
5 MA.912.G In circle below,. A. B. C. D. Based on this information, which statement must be true? MA.912.G A 14foot ladder is leaning against a house so that its top touches the top of the wall. The bottom of the ladder is 8 feet away from the wall. Which of these can be used to find the height of the wall? A. In a right triangle with a 14foot leg and an 8foot leg, find the length of the hypotenuse. B. In a right triangle with a 14foot leg and an 8foot leg, find the altitude to the hypotenuse. C. In a right triangle with a 14foot hypotenuse and an 8foot leg, find the length of the other leg. D. In a right triangle with a 14foot hypotenuse and an 8foot leg, find the altitude to the hypotenuse. MA.912.G In QRS, is an altitude. Which additional condition would NOT be sufficient to prove that QR = SR? A. T is the midpoint of. B. bisects QRS. C. TS = 2 cm D. RT = 4 cm Page 5 of 22
6 MA.912.G Within a square section of land, a landscaper will build a path, as represented by the shaded section in the diagram below. Which measure is closest to the value of y? A. 5.5 ft. B. 3.1 ft. C. 4.3 ft. D. 7.5 ft. MA.912.T A tree s shadow is 4.8 m long on level ground, as shown in the diagram. The angle of elevation from the tip of the shadow to the sun is 50. Based on this information, which of the following is closest to the height of the tree? A. 3.6 m B. 5.7 m C. 3.1 m D. 7.5 m Page 6 of 22
7 MA.912.G Points A, B, C, and D are the vertices of a square. Points E and F are the centers of two congruent semicircles that are tangent to each other at point G. Which value is closest to the area of the shaded regions? A. 7.7 B. 4.3 C D MA.912.G The drawing below can be used to find, the width of Pearl Pond at its widest point. What is the value of? A. 34 meters B. 36 meters C. 45 meters D. 22 meters Page 7 of 22
8 MA.912.G The drawing below shows Jeremy s mailbox and the brace he used to secure it to the post. If the length of the brace is approximately 18 inches, which is closest to, the distance between the bottom of the mailbox and the point on the post where Jeremy secured the brace? A. 17 in. B. B 25 in. C. C 19 in. D. D 11 in. MA.912.T From the observation deck of a lighthouse 70 meters above sea level, the lighthouse keeper can see a fishing boat at a 25degree angle of depression. What is the horizontal distance, to the nearest meter, from the base of the lighthouse to the fishing boat? A. 32 m B. 77 m C. 150 m D. 165 m Page 8 of 22
9 MA.912.G Look at the cylinder shown below. What is the total surface area of this cylinder in terms of? A. 273 B. 371 C. 322 D. 956 MA.912.G Which of the following is true of all squares and all rectangles? I. All squares and all rectangles are equilateral. II. All squares and all rectangles are equiangular. III. All rectangles are squares. A. II only B. III only C. II and III only D. I, II, and III MA.912.G Mr. Franco is making a triangular cement slab and needs to set boards before he can pour the cement. He has already set two boards that are 5 feet and 8 feet in length. What is a reasonable range for the length of the third board that Mr. Franco could set for this triangular cement slab? A. The third board needs to be greater than 3 feet in length. B. The third board can be between 3 feet and 13 feet in length. C. The third board needs to be less than 13 feet in length. D. The third board can be 3 feet or 13 feet in length. Page 9 of 22
10 MA.912.G Matthew correctly constructed a model of a right triangle with the largest dimensions possible to fit in a cube, as shown in the figure below. If each side of the cube measures eight centimeters, what is the approximate length of the hypotenuse of this right triangle? A cm B cm C cm D. 16 cm MA.912.G The dimensions of 3 connected stores are shown below. How many square feet of floor space are used by the 3 stores? A. 9,600 B. 11,280 C. 21,141 D. 42,021 Page 10 of 22
11 MA.912.G Lisa was on vacation in California and saw this sign next to a large tree in the forest. After looking at the tree, she concluded that the diameter was correct but that the circumference was incorrect. Which explanation shows why Lisa concluded that the circumference on the sign was incorrect? A. The circumference should be slightly larger than the diameter. B. The circumference should be slightly larger than 3 times the radius. C. The circumference should be slightly larger than 3 times the diameter. D. The circumference should be slightly larger than 3 times the radius squared. MA.912.T Which expression can be used to find the length of in centimeters? A. B. C. D. Page 11 of 22
12 MA.912.G Points P, Q, R, and T all lie on circle W, as shown below. If circle W has an approximate area of 618 square centimeters and SW = 12 centimeters, which is closest to the length of? A. 24 cm B. 15 cm C. 37 cm D. 7 cm MA.912.G ΔXYZ has a right angle at point Y. Point W is between points X and Z. is perpendicular to. According to this information, which of the following is true? A. ΔZYW ΔXYZ B. ΔYZW ΔXYZ C. ΔXWY ΔXYZ D. ΔWYZ ΔXYZ MA.912.G In the figure below, Elm St. is to be constructed parallel to Main St. What is the value of? A. 70 B. 110 C. 120 D. 130 Page 12 of 22
13 MA.912.G Which statement about a triangular prism is true? A. A triangular prism has 4 faces, 6 edges, and 4 vertices. B. A triangular prism has 3 faces, 6 edges, and 3 vertices. C. A triangular prism has 5 faces, 9 edges, and 6 vertices. D. A triangular prism has 6 faces, 11 edges, and 8 vertices. MA.912.G Which type of polygon can never be equiangular? A. parallelogram B. obtuse triangle C. pentagon D. equilateral octagon MA.912.G The top of a bench has a length of 5 ft. and a width of 2 ft. A second bench is similar to the first bench. The top of the second bench is 3 ft. wide. What is the length of the top of the second bench? A. 6 ft. B. 7 ft. C. 4.5 ft. D. 7.5 ft. MA.912.G Lines r, t, n, and v intersect as shown to form isosceles trapezoid ABCD. Which expression represents the measure of in degrees? A. B. C. D. Page 13 of 22
14 MA.912.G In quadrilateral, and. Which of the following statements is a reasonable conclusion? A. B. Quadrilateral is a rectangle. C. Quadrilateral is an isosceles trapezoid. D. MA.912.G Study the figure below. Which theorem can be used to prove that ΔKLN ΔMNL? A. SideSideSide B. SideSideAngle C. HypotenuseLeg D. AngleAngleSide MA.912.G The area of a larger square is 16 times the area of a smaller square. How many times as long is the base of the larger square than the base of the smaller square? A. 2 times as long B. 4 times as long C. 8 times as long D. 16 times as long MA.912.G What is the difference between the sum of the measures of the interior angles of a regular pentagon and the sum of the measures of the exterior angles of a regular pentagon? A. 36 B. 72 C. 108 D. 180 Page 14 of 22
15 MA.912.G The figure below is a circle inside a rectangle. What is the area, to the nearest square inch, of the shaded region of the figure? A. 32 square inches B. 41 square inches C. 51 square inches D. 88 square inches MA.912.G What is an equation of the circle with center (5,4) and a radius of 7? A. B. C. D. MA.912.G The measure of an interior angle of a regular polygon is 120. How many sides does the polygon have? A. 6 B. 5 C. 4 D. 3 MA.912.G Triangle ABC is similar to triangle DEF. The lengths of the sides of ABC are 5, 8, and 11. What is the length of the shortest side of DEF if its perimeter is 60? A. 10 B C. 20 D Page 15 of 22
16 MA.912.G A company is designing a flotation device made of foam. The shape of the design is modeled below. Which net can be folded to form the shape of the flotation device? A. B. C. D. MA.912.G Kristen is designing a triangular ramp so she can practice jumps with her bike. She has three pieces of wood. Which could be the possible measurements of these three pieces? A. 2 feet, 5 feet, 9 feet B. 3 feet, 4 feet, 8 feet C. 3 feet, 6 feet, 8 feet D. 4 feet, 5 feet, 9 feet MA.912.G Sarah is watching a monitor that shows the locations of ships in the ocean. These locations are displayed on a coordinate grid. To avoid collisions, a safety zone with a radius of 4 units is kept around each ship. Sarah notices one ship at point (2, 3). Which equation represents the edge of the safety zone for this ship? A. B. C. D. Page 16 of 22
17 MA.912.G The door of the cabinet shown below can open to a maximum angle of 90. What is the length of the arc through which the door swings? A inches B inches C inches D inches MA.912.G A circle s center is at (2, 3), and one point on the circle is (3, 5). What is the equation of the circle? A. B. C. D. Page 17 of 22
18 50. A rhombus and a rectangle are shown below. Which property is true for the rhombus but not true for the rectangle? A. Opposite angles are congruent. B. Opposite angles are supplementary. C. Diagonals are congruent. D. Diagonals are perpendicular. MA.912.G The diameter of a sphere is 30 centimeters. Which of the following is closest to the surface area of the sphere? A. 377 square centimeters B. 2,827 square centimeters C. 11,310 square centimeters D. 45,239 square centimeters MA.912.G The storage cabinet shown below is in the shape of a rectangular solid. All six faces of the storage cabinet are to be painted. What is the surface area of the storage cabinet to the nearest hundredth of a square foot? A B C D Page 18 of 22
19 MA.912.D Which statement is logically equivalent to if the juice spilled on the chair, then there is a stain on the chair? A. If there is not a stain on the chair, then the juice did not spill on the chair. B. If the juice did not spill on the chair, then there is not a stain on the chair. C. The juice spilled on the chair if and only if there is a stain on the chair. D. If there is a stain on the chair, then the juice spilled on the chair. MA.912.D Which statement is the inverse of the statement below? If you do your homework, then you will play a game A. If you play a game, then you do your homework. B. If you do not do your homework, then you will not play a game. C. If you don t a play game, then you don t do your homework. D. If you do not do your homework, then you will play a game. MA.912.D Which of the following is the contrapositive of the conditional statement below? If Alex gets at least a B on the final test, then he will pass the class A. If Alex gets a C or less on the final test, then he will not pass the class. B. If Alex does not get at least a B on the final test, then he will not pass the class. C. If Alex does not pass the class, then he did not get at least a B on the final test. D. Alex will pass the class if and only if he gets at least a B on the final test. MA.912.D Write the converse of the following statement. If two angles are vertical, then they are congruent. A. If two angles are not vertical, then they are not congruent. B. If two angles are not vertical, then they are congruent. C. If two angles are congruent, then they are vertical. D. If two angles are not congruent, then they are not vertical. MA.912.G Quadrilateral JKLM has vertices J(4, 1), K(1, 2), and L(6, 2). For what coordinates of point M is JKLM a parallelogram? A. (3, 2) B. (3, 1) C. (4, 0) D. (4, 1) Page 19 of 22
20 MA.912.G Circus elephants perform tricks on crates with sides that form quadrilaterals. In order to maximize the amount of weight that the crate can hold, the quadrilaterals must meet the following requirements: I. Exactly one pair of opposite sides should be parallel. II. The base angles must be equal. III. The sides that are not parallel must be equal to each other. What kind of quadrilateral should the circus owner order? A. a kite B. a square C. a parallelogram D. an isosceles trapezoid MA.912.G Give the missing reason to complete the following proof. Statements A. Alternate Interior Angles Theorem B. AngleAngle Similarity Postulate C. Corresponding Angles Postulate D. Vertical Angles Theorem Reasons 1. Given 2. Given 4. SAS Postulate 5. C.P.C.T.C. 60. The rectangular prism below has a surface area of 2,176 square centimeters. A similar rectangular prism has a surface area of 544 square centimeters. How many centimeters long is the longest edge of the similar prism? Page 20 of 22
21 MA.912.G ABC and PQR are shown in the diagram below. Based on the information provided in the diagram, what is in degrees? MA.912.G What is the m M in quadrilateral LMNP? MA.912.G A wheel is being made with spokes that are 25 cm long, as shown in the figure below. The spokes meet at the center of the wheel and will be separated so that there is 5.6 cm along the curved part of the wheel between any two ends of a spoke. What is the central angle between any two consecutive spokes? Round your answer to the nearest degree. Page 21 of 22
22 MA.912.G In right triangle, is an altitude of the triangle that cuts the hypotenuse into two segments with lengths as shown. What is the height of triangle? MA.912.G A banner is composed of two congruent triangles and a rectangle, as shown below. What is the total area of the banner in square centimeters? Page 22 of 22
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