OGT Math Geometry

Question 1 Similar trapezoids are shown. What is the value of n? A. 10 B. 12 C. 15 D. 19

Question 2 A ramp is being built next to a 4-inch-high sidewalk, as shown in the diagram below. Which trigonometric relationship could be used to find the value of x? A.Cos 10o =4/x B. cos 10o =x/4 C. tan 10o =4/x D. tan 10o =x/4

Question 3 Points Q, R, and W are plotted on the coordinate grid. Where should point Z be plotted so that parallelogram QRWZ is formed? A. (–2, –6) B. (–1, –3) C. (3, –2) D. (2, –1)

Question 4 In which figure is the measure of ∠1 equal to 45º? C A B D   C A B D

Question 5 This net is folded to produce a three-dimensional object. Which object will this net produce? A B C D

Question 6 Trapezoid RSTU is shown on the grid. .  Question 6 Trapezoid RSTU is shown on the grid.   Which graph shows the image of trapezoid RSTU after it is translated 5 units up and 3 units to the left? C A D B

Question 7 An airline executive drew a sketch of a logo on a napkin. .  .  Question 7 An airline executive drew a sketch of a logo on a napkin. She gave the logo to a graphic designer so he could make a mathematically similar version with a computer drawing program. The center line of the new logo needs to be 10 centimeters long. Which of these proportions could the graphic designer use to find the value of y? A B C D

Question 8 When a marble hits a wall, it bounces off the wall at the same angle it hits the wall. If a marble hits a wall at a 22 degree angle, what is the measure of the angle between the two paths of the marble? A. 44° B. 68° C. 136° D. 158°

Question 9 A B C D The figure shows two views of the same object. .  .  Question 9 The figure shows two views of the same object.   Which net will make the figure shown? A B C D

Question 10 The coordinates of triangle KLM are K: (–2, –5), L: (0, 1) and M: (6, –2). What type of triangle is KLM? A. obtuse isosceles B. acute scalene C. right isosceles D. right scalene

Question 11 The figure shows a three-dimensional object when viewed from above. Which of these objects could the sketch represent? A. pentagonal pyramid B. rectangular prism C. square pyramid D. triangular prism

Question 12 The quadrilateral below is to be translated 6 units to the right and 3 units down. Which ordered pair is not the coordinates for a vertex of the translated image? A. (3, –4) B. (3, –1) C. (3, 2) D. (1, –1)

Question 13 Jake is using a computer program to design parts for a new car. He has outlined one-half of a part on a coordinate grid. Rather than drawing the second half, he plans to have the computer reflect this shape over the y-axis. Which of the following represents the 5 vertices of the reflected shape? A. (0, 0); (0, 2); (–1, 3); (–2, 3); (–2, 0) B. (0, 0); (0, 3); (–1, 3); (–2, 2); (–2, 0) C. (0, 0); (0, –3); (1, –3); (2, –2); (2, 0) D. (0, 0); (0, –3); (–1, –3); (–2, –2); (–2, 0)

Question 14 Points E, F, G, and H are midpoints of the sides of quadrilateral ABCD. If AC = 12 and BD = 8, what is the perimeter of quadrilateral EFGH? A. 96 B. 40 C. 20 D. 4

Question 15 The net creates a pyramid. B.  .  .  C.  Question 15 The net creates a pyramid. Which pyramid does this net create? A B C D

Question 16. In which figure is the measure of <1 NOT equal to 60o? .    B.    .    .  Question 16.  In which figure is the measure of  <1 NOT equal to 60o? C A B D

Question 17 Three vertices of a quadrilateral are (–1, –1), (1, 2) and (5, 2). When used as the last vertex, which point would make the quadrilateral a trapezoid? A. (3, 0) B. (3, –2) C. (–5, 0) D. (7, –1)

Question 18 What is the measure of angle D? A. 37° B. 45° C. 53° D. 74°

Question 19 Alicia is 5 feet tall. She casts a shadow that measures 6 1/2 feet long at the same time that a sculpture in the park casts a shadow 12 feet long. Which of the following is the approximate height of the sculpture? A. 9 feet B. 16 feet C. 27 feet D. 78 feet

.  Question 20 The figure shows the net for a three-dimensional object. When folded, which object will this net produce? A B C D

Question 21 A worker painted stripes for spaces in a parking lot. The worker first painted a center stripe that marked the front of the parking spaces. Then he painted parallel stripes marking the sides. Which angles will be congruent to angle 1 if all the side stripes are parallel? A. <2 and< 3 B. <2 and< 5 C.< 3 and <5 D. <4 and <5

Question 22 The shadow cast by a one-foot ruler is 8 inches long. At the same time, the shadow cast by a pine tree is 24 feet long. What is the height, in feet, of the pine tree? A. 3 feet B. 16 feet C. 36 feet D. 192 feet

Question 23 The vertices of a quadrilateral are (2, 2), (4, 6), (8, 2), and (10, 6). Which describes this quadrilateral? A. parallelogram B. rectangle C. rhombus D. square

Question 24 An electronics engineer is programming the computer that controls the circuit board cutting tools. He enters the coordinates of the vertices of a rectangular circuit board. The first three coordinates are (2, 0), (2, 6) and (6, 6). What are the coordinates of the fourth vertex? A. (0, 2) B. (0, 6) C. (6, 0) D. (6, 2)

Question 25 Susan is flying a kite behind her house. She drops her string holder, and the kite gets caught in the top of a tree. If the string makes a 44º angle with the ground, and the holder is 90 feet from the base of the tree, how tall is the tree, rounded to the nearest whole foot? A. 63 feet B. 65 feet C. 74 feet D. 87 feet

Question 26 Ms. Chen drew a diagram for a new patio in her backyard. The measure of <1 is 3 times as large as the measure of<2. What is the measure of <2? A. 45º B. 67.5º C. 120º D. 135º

Question 27 Joseph plans to tile his kitchen floor. All the tiles will be identical regular polygons. Joseph wants three tiles to meet at each vertex with no space left over. What shape of tiles should he use? A. pentagon B. hexagon C. triangle D. square

Question 28 Which figure is NOT a parallelogram? C A D B

Question 29 A student shines a light through a cutout of a triangle held parallel to a wall several feet straight in front of him, producing a similar image on the wall. What must the two triangles have in common? A. equal areas B. equal heights C. corresponding sides that are congruent D. corresponding angles that are congruent

Question 30 Points P, Q and R are shown below. These points are three vertices of a parallelogram. What are the coordinates of the fourth vertex of parallelogram PQRS? A. (4, 6) B. (5, 2) C. (8, –1) D. (9, 1)

Question 31 Daniel cut the corner off a cube as shown in the diagram below. Points A, B and C are the midpoints of the edges of the cube. What type of three-dimensional figure has been cut off? A. cone B. cube C. triangular prism D. triangular pyramid