TEKSING TOWARD STAAR Algebra I â Geometry ® MATHEMATICS Geometry TEKS/STAAR Spiraled Practice 1-20 Brenda DeBorde [email protected] Juanita Thompson [email protected] TEKSING TOWARD STAAR ©2012 TEKS/STAAR SPIRALED PRACTICE 1 Geometry 1. Caleb made a list of careers that he believes geometry is an important part of. His list included: a. b. c. d. e. architecture astronomy building construction graphic design navigation Which of the following statements is correct? A Caleb’s list is complete. B Caleb’s list is correct but incomplete. C Caleb’s list is incorrect. D Caleb’s list is incorrect and incomplete. 2. DABC is similar to DGHJ . B 8 A 6 4 C G H J What is the ratio of BC to HJ? F 3:4 G 4:3 H 2:1 J 1:2 TEKSING TOWARD STAAR © 2012 1. Cat 1/G.1B 2. Cat 2/G.5B 3. Cat 3/G.6B Page 1 TEKS/STAAR SPIRALED PRACTICE 1 Geometry 3. Which of the following could be the net of a rectangular prism? A C B D TEKSING TOWARD STAAR © 2012 1. Cat 1/G.1B 2. Cat 2/G.5B 3. Cat 3/G.6B Page 2 TEKS/STAAR SPIRALED PRACTICE 2 Geometry 1. A paperweight in the shape of a cylinder has a circumference of 8p centimeters. Its height is 12 centimeters. Circumference : 8p cm Height: 12 cm What is the total surface area of the paperweight? A 96p square centimeters B 102p square centimeters C 132p square centimeters D 128p square centimeters 2. Triangle ABC is similar to triangle DFE. If AB = 12 units, DF = 8 units, and BC = 9 units, what is the value of EF? A C F D B E F 10 units G 6 units H 7.5 units J 5 units 3. Which of the following statements is not true for all rectangles? A The sum of the four angles will be 360 degrees. B Opposite sides will be parallel and congruent. C When a diagonal is drawn, the angles will be bisected. D Adjacent sides will be perpendicular. TEKSING TOWARD STAAR Ó 2012 1. Cat 4/G.8D 2. Cat 5/G.11B 3. Cat 1/G.3B Page 1 TEKS/STAAR SPIRALED PRACTICE 3 Geometry 1. Which expression represents the perimeter of the triangle below? 2x + 3 3x A 5x + 3 C 6 x 2 + 9x B 7x + 6 D 7x + 3 2. Look at the sketch below. A B C E D F Which of the following points are collinear? F A, B and D H A, C and E G B, D and E J B, D and F 3. A circle has a circumference of 16 p inches. Which of the following represents the area of the circle? C = 16p in. A 64p square inches B 16p square inches C 64 square inches D 8p square inches TEKSING TOWARD STAAR Ó 2012 1. Cat 2/G.4A 2. Cat 3/G.7A 3. Cat 4/G.8A Page 1 TEKS/STAAR SPIRALED PRACTICE 4 Geometry 1. A triangle with vertices ( - 3, 6), (5, 6) and (1, - 2) is shown below. y 10 9 8 7 6 5 4 3 2 1 -10 -9 -8 –7 -6 -5 -4 -3 -2 -1 -1 1 2 3 4 5 6 7 8 9 10 x -2 -3 -4 -5 -6 -7 -8 -9 -10 Which triangle below is similar to the figure above? y A y 10 10 9 9 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 -10 -9 -8 –7 -6 -5 -4 -3 -2 -1 1 -1 2 3 4 5 6 7 8 9 10 x C 1 -10 -9 -8 –7 -6 -5 -4 -3 -2 -1 -2 -2 -3 -3 -4 -4 -5 -5 -6 -6 -7 -7 -8 -8 -9 -9 -10 -10 10 10 9 9 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 -10 -9 -8 –7 -6 -5 -4 -3 -2 -1 TEKSING TOWARD STAAR -1 1 2 3 4 5 6 7 8 9 10 x D 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 -10 -9 -8 –7 -6 -5 -4 -3 -2 -1 -1 -2 -2 -3 -3 -4 -4 -5 -5 -6 -6 -7 -7 -8 -8 -9 -9 -10 -10 Ó 2012 1 x y y B -1 1. Cat 5/G.11A 2. Cat 1/G.1C 3. Cat 2/G.5D x Page 1 TEKS/STAAR SPIRALED PRACTICE 4 Geometry 2. In a non-Euclidean geometry called taxicab geometry we are looking at a geometry that lies on a square grid. The only paths you can travel are horizontal and vertical paths like the streets on a grid as shown below. . . . . . A. . . . . . . . . . . . . . . . . . .B . . . . . . . . . . . . . . . . . . . . . Which statement correctly compares the distance between points A and B using taxicab geometry and Euclidean geometry? F The taxicab distance is 2 units less than the Euclidean distance. G The taxicab distance is 2 units more than the Euclidean distance. H The taxicab distance is 1 unit less than the Euclidean distance. J The taxicab distance is 1 unit more than the Euclidean distance. 3. The numbers 10, 24 and 26 form a Pythagorean triple. Which of the following also form a Pythagorean triple? A 15, 36, 39 B 30, 70, 78 C 40, 96, 102 D 5, 12, 14 TEKSING TOWARD STAAR Ó 2012 1. Cat 5/G.11A 2. Cat 1/G.1C 3. Cat 2/G.5D Page 1 TEKS/STAAR SPIRALED PRACTICE 5 Geometry 1. Parallelogram ABCD has vertices A ( - 6, - 2), B ( - 2, - 6), C (6, - 6) and D (2, - 2). slope of diagonal AC of the parallelogram ABCD? A 1 3 B - C 3 D -3 What is the 1 3 2. The height of a cone measures 14 centimeters and the radius of the cone measures 5 centimeters. 14 cm 5 cm Which of the following best represents the volume of the cone? F 79 cm 3 G 366 cm 3 H 467 cm 3 J 1,099 cm 3 3. Mrs. Jones has a rectangular flower bed that is 65 inches long and 36 inches wide. She increases the length by 9 inches and the width by 5 inches to create a new flower bed. Which of the following best describes the relationship of the perimeter of the new flower bed and the old flower bed? A The new flower bed has a perimeter that is 14 inches more than the perimeter of the old flower bed. B The new flower bed has a perimeter that is 45 inches more than the perimeter of the old flower bed. C The new flower bed has a perimeter that is 28 inches more than the perimeter of the old flower bed. D The old flower bed has a perimeter that is 28 inches more than the perimeter of the new flower bed. TEKSING TOWARD STAAR © 2012 1. Cat 3/G.7C 2. Cat 4/G.8D 3. Cat 5/G.11D Page 1 TEKS/STAAR SPIRALED PRACTICE 6 Geometry 1. The construction of a perpendicular at point P on line r is shown below. Q S T r P Which of the following conjectures will not be true? A P is the midpoint of ST B Q is equidistant from T and S. C Points Q, T, and S will form an isosceles triangle. D ÐQSP will be a right angle. 2. The table below shows the length of a diagonal of a square and the area of the square. Squares Length of diagonal 1 2 3 4 n Area 0.5 2 4.5 8 From the pattern above, which of the following would represent the area of a square with a diagonal length of n? F 2n G n ¸2 H n2 ¸ 2 J 2n - 2 TEKSING TOWARD STAAR © 2012 1. Cat 1/G.2A 2. Cat 2/G.5A 3. Cat 3/G.6C Page 1 TEKS/STAAR SPIRALED PRACTICE 6 Geometry 3. Which three-dimensional figure has the front, side and top views shown below? Front Side A Top C Front Front B D Front Front TEKSING TOWARD STAAR © 2012 1. Cat 1/G.2A 2. Cat 2/G.5A 3. Cat 3/G.6C Page 2 TEKS/STAAR SPIRALED PRACTICE 7 Geometry 1. A spinner with a 10 centimeter radius has 4 sectors. The green sector has a central angle of 150 ° . The red sector has a central angle of 80 ° . The blue sector has a central angle of 60 ° . The brown sector has a central angle of 70 ° . Green Brown Blue Red What is the probability that the spinner will land on green or blue? A 7 18 C 5 12 B 7 12 D 11 18 2. A right triangle has sides of 3, 4, and 5. Which of the following could not be the sides of a right triangle that would be similar to the original triangle? F 10, 24, 26 H 15, 20, 25 G 12, 16, 20 J 3. Look at the Venn diagram for triangles below. 7.5, 10, 12.5 Which conjecture is not true? TRIANGLES Right Scalene Isosceles Equilateral A A triangle can be a scalene right triangle. B An isosceles triangle can be a right triangle. C All equilateral triangles are isosceles. D A right triangle can be equilateral. TEKSING TOWARD STAAR © 2012 1. Cat 4/G.8E 2. Cat 5/G.11C 3. Cat 1/G.2B Page 1 TEKS/STAAR SPIRALED PRACTICE 8 Geometry 1. The class was given the following figure. The students were asked to create three new drawings of the figure showing in the figure through a progression of transformations in the order of : translation, rotation, reflection. Four students' drawings are shown below. Which student correctly drew the movements in order? A B C D TEKSING TOWARD STAAR © 2012 1. Cat 2/G.5C 2. Cat 3/G.7B 3. Cat 4/G.8F Page 1 TEKS/STAAR SPIRALED PRACTICE 8 Geometry 2. The diagonals of a rhombus are perpendicular. The equation of a diagonal of a rhombus is 5 x + 3y = 8 . Which of the following could be the equation of the other diagonal? F 3x + 5y = -6 G 3 x - 5y = 5 H 5 x - 3y = 6 J 5 x + 3y = 3 3. A carpenter has a piece of lumber that is 1.5 meters long. He needs a piece that is 4.5 feet long. He needs to know if his piece is long enough. Which of the following best describes his situation? (1 inch is approximately 2.54 centimeters.) A Yes, he has enough and he will have about 13 centimeters left. B Yes, he has enough and he will have about 5 centimeters left. C No, he does not have enough. He will need a piece that is about 13 centimeters longer. D No, he does not have enough. He will need a piece that is about 5 centimeters longer. TEKSING TOWARD STAAR © 2012 1. Cat 2/G.5C 2. Cat 3/G.7B 3. Cat 4/G.8F Page 2 TEKS/STAAR SPIRALED PRACTICE 9 Geometry 1. A triangle has an area of 36 square units. If the dimensions of the triangle are increased to 1 1 3 their original size, what will be the area of the new triangle? A 48 square units B 72 square units C 64 square units D 192 square units 2. What is the contrapositive of the following conditional statement? If a rectangle is a square, then it has congruent adjacent sides. F A rectangle is a square if it has congruent adjacent sides. G A rectangle is not a square if and only if it does not have congruent adjacent sides. H If a rectangle is not a square, then it does not have congruent adjacent sides. J If the adjacent sides of a rectangle are not congruent, then the rectangle is not a square. 3. The figures below represent similar rectangles. 2.5 units 5 units 5 units 10 units 7.5 units 15 units Which of the following represents the dimensions of a rectangle that would not belong to this set of similar rectangles? A 4 units by 8 units B 3.5 units by 7 units C 10 units by 20 units D 1 unit by 3 units TEKSING TOWARD STAAR © 2012 1. Cat 5/G.11D 2. Cat 1/G.3A 3. Cat 2/G.5B Page 1 TEKS/STAAR SPIRALED PRACTICE 10 Geometry 1. A square pyramid is intersected by plane X parallel to the base of the pyramid as shown below. A H G X I J D E C F If AG = 0.4AC, which of the following statements can be justified? A The area of the base of the smaller pyramid will be 0.4 times the area of the larger pyramid. B The volume of the smaller pyramid will be 0.4 times the volume of the larger pyramid. C The smaller pyramid will be similar to the larger pyramid with a scale factor of 0.4. D AG AD = AC AH 2. If l ^ n , what is the value of x? l (6y - 4 x)° F ( x + 3y )° n 25 G 15 H 30 J 20 TEKSING TOWARD STAAR Ó 2012 1. Cat 3/G.6A 2. Cat 4/G.9A 3. Cat 5/G.11A Page 1 TEKS/STAAR SPIRALED PRACTICE 10 Geometry 3. Triangle ABC is dilated to create triangle A′B′C′ as shown below on the grid below. y 10 9 B′ B 8 7 6 5 4 C′ 3 A′ 2 1 -10 -9 -8 –7 -6 -5 -4 -3 -2 -1 C-1 1 2 3 4 5 6 7 -2 -3 8 9 10 x A -4 -5 -6 -7 -8 -9 -10 Which statement appears to be true? A The center of dilation used to create triangle A′B′C′ was ( - 7, 8). B The two triangles are congruent. C The scale factor used to create triangle A′B′C′ was 0.5. D Triangle ABC was reduced in size to create triangle A′B′C′. TEKSING TOWARD STAAR Ó 2012 1. Cat 3/G.6A 2. Cat 4/G.9A 3. Cat 5/G.11A Page 2 TEKS/STAAR SPIRALED PRACTICE 11 Geometry 1. Larry was given the following statements. Linear pairs are supplementary. Ð2 and Ð3 are a linear pair. Using the given statements, which of following conclusions would be a valid conclusion for Larry to make? A Ð2 and Ð3 are congruent. C Ð2 is acute. B Ð2 and Ð3 are not supplementary. D Ð2 and Ð3 are supplementary. 2. Jamie wants to use one figure to tessellate a plane for a project. Which of the following should she not choose for her project? F Equilateral triangle G Regular hexagon H Square J Regular pentagon 3. Which net represents the surface area of the pentagonal prism? A C B TEKSING TOWARD STAAR D © 2012 1. Cat 1/G.3C 2. Cat 2/G.5C 3. Cat 3/G.6B Page 1 TEKS/STAAR SPIRALED PRACTICE 12 Geometry 1. If CD is a base and CF is a leg of isosceles trapezoid CDEF, then which statement must be true? 2. A CD and CF are perpendicular. B CD and EF are parallel. C CF and DE are parallel. D DE and EF are parallel. In the diagram below, CD is the altitude to the hypotenuse of right traingle ABC. A D B C Which pair of triangles listed below are similar triangles? F DADC and DBDC G DADC and DABC H DCDA and DBDC J DABC and DBDC 3. Which of the following is an example of inductive reasoning? A All right triangles contain one right angle. Triangle ABC is a right triangle; therefore it will contain a right angle. B Martin observed a number pattern of 0, 10, 21, 33 and decided the next two terms would be 46 and 60. C If a triangle is isosceles, it has two congruent sides. Triangle ABC is isosceles; therefore it has two congruent sides. D If Barbara attends study sessions, she does well on her tests. If she does well on her tests, her mother rewards her. Barbara attends study sessions; therefore, she does well on her tests and receives a reward from her mother. TEKSING TOWARD STAAR © 2012 1. Cat 4/G.9B 2. Cat 5/G.11C 3. Cat 1/G.3D Page 1 TEKS/STAAR SPIRALED PRACTICE 13 Geometry 1. Rhombus ABCD is shown below. The measure of angle ABC is 45 ° . Segment AF represents the height of the rhombus. If AF is 10 meters, which of the following best represents the length of a side of the rhombus? A B 10 meters D A 10 meters B 5 2 meters C 10 2 meters F C D 5 meters 2. One side of a rhombus is defined by the equation 3x - 4y = 2 . Which of the following equations could define the opposite side of the rhombus? F 4 x - 3y = 3 G 3x - 4y = 5 H 6 x + 8y = 6 J 4 x - 3y = -5 3. LK , EL , DK and ED are segments of circle P as shown below. These segments are called chords. E L K M P D DEML is similar to DKMD . Which of the following statements is always true? A Ð LKD is congruent to Ð KLE. B LK is longer than ED . C EM ´ MD = KM ´ ML D ED is longer than a diameter. TEKSING TOWARD STAAR © 2012 1. Cat 2/G.5D 2. Cat 3/G.7B 3. Cat 4/G.9C Page 1 TEKS/STAAR SPIRALED PRACTICE 14 Geometry 1. If a right triangle has sides of 5, 12 and 13 centimeters, which of the following could be the side lengths of a triangle similar to it? A 10, 24, 25 B 9, 24, 26 C 17.5, 42, 45.5 D 20, 48, 56 2. The angles of a triangle are 53, 75 and x degrees. The following statements are to be used to find x. 1. 2. 3. 4. 128 + x = 180 x = 52 128 + x – 128 = 180 – 128 53 + 75 + x = 180 Which order should the steps be used to find x? F 1, 3, 4, 2 G 4, 1, 3, 2 H 2, 1, 3, 4 J 4, 3, 1, 2 3. A rectangle has a perimeter of 102 inches. The length of the rectangle is 3.25 times as long as the width of the rectangle. Using w for the width and y for the length, which of the following pairs of equations could be used to find the dimensions of the rectangle? A ìw + y = 51 í îy = 3.25w B ìw + y = 102 í îw = 3.25y C ìw + y = 51 í îw = 3.25 ¸ y ü ý þ D ì2w + 2y = 102 í î y = 3.25 + w ü ý þ TEKSING TOWARD STAAR ü ý þ ü ý þ © 2012 1. Cat 5/G.11B 2. Cat 1/G.3E 3. Cat 2/G.4A Page 1 TEKS/STAAR SPIRALED PRACTICE 15 Geometry 1. Two points A and B are equidistant from point C. However, they are not collinear points. Point A has coordinates ( - 5, 3) and point B has coordinates (1, 8). Point C has coordinates (x, y). Which of the following is an appropriate representation for relationship among A, B, and C? A ( x - 1)2 - (y - 8)2 = (x + 5)2 - (y - 3)2 C ( x - 1)2 + (y - 8)2 = B ( x - 8)2 + (y - 1)2 = ( x - 5)2 + (y + 5)2 D ( x - 1) + (y - 8) = ( x + 5)2 + (y - 3)2 ( x + 5) + (y - 3) 2. A candy box shaped like a right rectangular prism is shown below. Which of the following statement is not true about the prism? F The prism has exactly 6 faces. G The prism has exactly 8 vertices. H The prism has exactly 10 edges. J All the faces are rectangles. 3. In the figure below, segment QR is perpendicular to QP and RS and DPQR Q ~ DQRS . P 12 feet R S 16 feet What is the length of QP ? A 10 feet C 15 feet B 20 feet D 9 feet TEKSING TOWARD STAAR © 2012 1. Cat 3/G.7C 2. Cat 4/G.9D 3. Cat 5/G.11C Page 1 TEKS/STAAR SPIRALED PRACTICE 16 Geometry 1. The measures of an exterior angle for 4 regular polygons are shown below in the sketch. 120° 90° 72° 60° Which expression best represents the measure of an exterior angle of a regular polygon with n sides? A n 360 B (n - 2)(180) C 360 n D 180 n 2. In taxicab geometry the distance between two points, ( x1 , y1 ) and ( x2 , y2 ), is x1 - x2 + y1 - y2 . In Euclidean geometry the distance between two points, ( x1 , y1 ) and ( x2 , y2 ), is ( x2 - x1 )2 + (y2 - y1 )2 . For which of the following points would the taxicab distance and the Euclidean distance be the same? F (1, 1) and (2, 2) G (5, 0) and ( 6, 10) H (4, 0) and ( - 4, 0) J (6, 1) and (3, 2) 3. If a plane intersects a cylinder perpendicular to the bases and passes through the centers of the bases, which of the following best describes the intersection? A circle B parallelogram C rectangle D semicircle TEKSING TOWARD STAAR © 2012 1. Cat 2/G.5A 2. Cat 1/G.1C 3. Cat 3/G.6A Page 1 TEKS/STAAR SPIRALED PRACTICE 17 Geometry 1. Triangle ABC is shown below. y 10 9 8 B 7 6 5 4 3 2 A 1 -10 -9 -8 –7 -6 -5 -4 -3 -2 -1 -1 -2 1 2 3 4 5 6 7 8 9 10 x C -3 -4 -5 -6 -7 -8 -9 -10 Triangle ABC is translated so that C (3, - 1) is mapped to C′ (1, - 4). represents A′? A (7, 3) B (4, 3) C ( - 1, 1) Which ordered pair best D ( - 1, - 1) 2. A rectangle has dimensions of 5 inches and 8 inches. If the dimensions are doubled, what will be the perimeter of the new rectangle? F 26 inches G 40 inches H 13 inches J 52 inches 3. Euclidean Geometry has three terms that are called undefined terms. Two of the terms are point and plane. The third term is A ray B line segment C line D angle TEKSING TOWARD STAAR © 2012 1. Cat 4/G.10A 2. Cat 5/G.11D 3. Cat 1/G.1B Page 1 TEKS/STAAR SPIRALED PRACTICE 18 Geometry 1. When the angle of elevation of the sun measures 45 ° , a tower casts a 30-meter shadow. x 45 ° 30 30mmeters Which of the following is the best estimate of the height of the tower, x? A 30 m C 17.3 m B 26 m D 45 m 2. Rectangle ABCD has diagonals that intersect at point E. A B (8, 6) E C D ( - 5, - 3) Which of the following best describe point E? F (3, 3) H G (1.5, 3) J (1.5, 1.5) ( - 1.5, - 1.5) 3. If P is the midpoint of US and TR , which congruency statement can be verified with deductive reasoning? T U P S R A DPUT @ DRSP C DPUT @ DPSR B DPTU @ DPSR D DUPT @ DRSP TEKSING TOWARD STAAR © 2012 1. Cat 2/G.5D 2. Cat 3/G.7C 3. Cat 4/G.10B Page 1 TEKS/STAAR SPIRALED PRACTICE 19 Geometry 1. The radius of the larger sphere shown below was multiplied by a factor of 1 to produce a smaller 4 sphere. Radius = Radius = r 1 r 4 How does the surface area of the smaller sphere compare to the surface area of the larger sphere? A B 1 as large. 4 1 The surface area of the smaller sphere is as large. The surface area of the smaller sphere is p 1 as large. 8 1 D The surface area of the smaller sphere is as large. 16 C The surface area of the smaller sphere is 2. The construction below shows ÐACB with bisecting ray CD. A D C B Which of the following statements is not valid based on the construction? F m ÐACD = 1 2 m ÐACB H m ÐACB = 2m ÐDCB G m ÐACD = m ÐDCB J m ÐDCB = 2m ÐBCA 3. Identify which of the following sets of numbers are Pythagorean triples. A 2, 4, 6 C 5, 12, 13 B 0.3, 0.4, 0.5 D TEKSING TOWARD STAAR © 2012 1. Cat 5/G.11D 1, 1, 2 2. Cat 1/G.2A 3. Cat 2/G.5D Page 1 TEKS/STAAR SPIRALED PRACTICE 20 Geometry 1. Which point plotted below best represents 3 A Point M B Point N C Point O 3.25 15 ? M N 3.5 3.75 O P 4 D Point P 2. A right triangle has a hypotenuse of 26.2 inches and a leg of 17.2 inches. Which of the following best represents the length of the other leg? F 9.0 inches G 19.8 inches H 31.3 inches J 17.9 inches 3. If the length and height only of a rectangular prism are doubled, what effect will this have on the volume of the prism? l 2h h w w 2l A The new volume will be twice the original volume. B The new volume will be four times the original volume. C The new volume will be eight times the original volume. D The new volume will increase by 4 cubic units. TEKSING TOWARD STAAR © 2012 1. Cat 3/G.7A 2. Cat 4/G.8C 3. Cat 5/G.11D Page 1
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