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Geometry February Break Extra Credit Assessment ID: ib.573505 Directions: Answer the following question(s). 1 A. B. C. D. 2 A. B. C. D. 3 What does the symbol represent? 4 segment AB line AB Ray AB Ray BA "Two rays sharing a common endpoint" is the definition of which term? angle chord line segment secant If triangle ABC is rotated 90 degrees clockwise about the origin, what are the coordinates of B'? A. B. C. D. 5 A. B. C. D. In this diagram where is the line of reflection? (–4, –1) (4, 1) A. B. C. D. x=0 x=1 y=2 y = 3.5 The vertices of parallelogram ABCD are A(2 , 1), B(3 , 4), C(5 , 3), and D(4 , 0). ABCD is reflected over the x–axis to create parallelogram QRST. What are the coordinates of QRST? Q(–2 , 1), R(–3 , 4), S(–5 , 3), T(–4 , 0) Q(–2 , –1), R(–3 , –4), S(–5 , –3), T(–4 , 0) Q(1 , 2), R(4 , 3), S(3 , 5), T(0 , 4) Q(2 , –1), R(3 , – 4), S(5 , –3), T(4 , 0) (1, –4) (1, 4) Illuminate Itembank™ Generated On February 8, 2016, 3:59 PM PST Continue: Turn to the next page. Page 1 Geometry February Break Extra Credit Assessment ID: ib.573505 Directions: Answer the following question(s). 6 In this diagram, what is the BEST description of the transformation shown? 8 Equilateral triangle ABC is shown below. Triangle ABC is then rotated 60 degrees clockwise about vertex C to produce triangle A'B'C'. Select each statement that is true based on the definition of a rotation. A. Vertex C and vertex C' are located in the same place. B. The measure of ∠B'C'A' is 120° since 60 + 60 = 120. C. The measure of ∠B' is 60° since the measure of ∠B is 60°. D. The measure of ∠BCB' is 60° since 60° is the angle of rotation. A. B. C. D. Reflection 9 Rotation Translation Which statements are true for all rotations about the origin? Select three that apply. A. Angles are taken to angles of the same measure. Dilation B. Perpendicular lines are taken to perpendicular 7 A. B. C. D. The vertices of ∆ABC are A(–4, 2), B(6, 6), C(2, 7). A translation maps point A to the point A'(6, –3). If B and C are mapped by the same translation, what are the coordinates of B' and C'? lines. C. Circles are taken to circles of the same center and radius. D. Line segments are taken to line segments of the same length. B'(–4, 11), C'(–8, –12) B'(8, 5), C'(4, 6) 10 B'(12, 3), C'(8, 4) B'(16, 1), C'(12, 2) A. B. C. D. Illuminate Itembank™ Generated On February 8, 2016, 3:59 PM PST A triangle with coordinates A(1, 1), B(4, 2), C(3, 5) is translated three units down and five units to the left. What are the coordinates of the new triangle? A'(–2, –4), B'(1, –3), C'(0, 0) A'(–4, –2), B'(–1, –1), C'(–2, 2) A'(–4, –2), B'(–7, –3), C'(–6, 0) A'(–4, –2), B'(–1, –3), C'(–2, –6) Continue: Turn to the next page. Page 2 Geometry February Break Extra Credit Assessment ID: ib.573505 Directions: Answer the following question(s). 11 A. B. C. D. 12 Name the type of congruence transfomation from XYZ to X'Y'Z'. 13 reflection rotation In the figure above, the black shape is a dilation of the green shape. What is the scale factor of the dilation, and what is the center of the dilation? translation dilalation Calculate the length of the side LN given the following data for 37°. Sin 37° = 0.602 Cos 37° = 0.790 Tan 37° = 0.754 A. scale factor: 3; center: 3, 0 B. scale factor: 3; center: 0, 0 C. scale factor: 2; center: 1/2, −1 D. scale factor: 11/2 ; center: 11/2, −3 E. scale factor: 1/2 ; center: 0, 0 F. scale factor: 1/2 ; center: 3, 0 G. scale factor: 1/3 ; center: 0, 0 14 A. B. C. D. 53 9.97 7.96 7.51 Illuminate Itembank™ Generated On February 8, 2016, 3:59 PM PST A. B. C. D. Determine which pair of trigonometric values is equivalent. cos 38°, sin 38° cos 65°, sin 25° sin 71°, sin 19° cos 113°, cos 67° Continue: Turn to the next page. Page 3 Geometry February Break Extra Credit Assessment ID: ib.573505 Directions: Answer the following question(s). 17 15 Which congruence statement(s) can be proven using the givens and the figure above? A. ΔQRP ≅ ΔSRT only B. ΔRQP ≅ ΔTRS only C. ΔPQR ≅ ΔSTR only D. All three of the congruence statements above Which of the following could be a two– dimensional figure that results when a plane intersects this right circular cylinder? Select three that apply. A. B. C. D. 18 can be proven. 16 A right circular cylinder is shown below. Triangle PQR is shown below. circle ellipse triangle rectangle Jeffry needs to create a triangle for his woodworking project. He knows that one side of the triangle needs to be 15 inches long and the hypotenuse needs to be 45 inches long. He has diagrammed his project (below) and needs help to find the measure of angle Z where he plans to cut his board. When triangle PQR is rotated about side QR, which of the following three–dimensional figures is created? A. B. C. D. cone cylinder pyramid triangular prism A. B. C. D. Illuminate Itembank™ Generated On February 8, 2016, 3:59 PM PST 70.5° 19.5° 18.4° 78.2° Continue: Turn to the next page. Page 4 Geometry February Break Extra Credit Assessment ID: ib.573505 Directions: Answer the following question(s). 19 Right triangle PQR is shown. 21 Declan is a park ranger at Niagara Falls. One day during his shift a man rides over the falls in a barrel. Declan knows that the distance from his observation tower station to the ranger station near the top of the falls is 736 feet. The man is at an angle of 126° with a line connecting the two stations. The ranger at thebridge station reports that the angle from hisstation to the man is 23°. How far is the man from Declan? Which trigonometric ratios are equivalent to 3 ? Select two that apply. 5 A. B. C. D. E. 20 cos P sin P cos R sin R tan R A right circular cone is shown below. The radius of the base of the cone is 30 cm and the height of the cone is 40 cm. A. B. C. D. 22 Select each shape that could be the two– dimensional cross–section of this cone. A. B. C. D. circle A. B. C. D. 558.4 feet 1661.5 feet 592.9 feet 394.8 "All points between and including two given points" defines which term below? ray plane circle line segment ellipse right triangle isosceles triangle Illuminate Itembank™ Generated On February 8, 2016, 3:59 PM PST Continue: Turn to the next page. Page 5 Geometry February Break Extra Credit Assessment ID: ib.573505 Directions: Answer the following question(s). 23 Look at this right triangle. 26 What is the slope of a line parallel to the line y=– 3 x + 3? 2 A. – 3 2 B. – 2 3 C. 2 3 D. 3 2 27 Find the volume of a sphere with a diameter of 22m. Round to the nearest tenth. What is the area of ΔDEF? A. B. C. D. 24 25 square units 50 square units 25 sqrt 5 square units 50sqrt 5 square units Select each transformation that carries a square onto itself. A. a reflection over one of the square's sides B. a reflection over one of the square's diagonals C. a rotation of 90° clockwise about the square's center D. a rotation of 180° clockwise about the square's center A. B. C. D. 28 E. a rotation of 180° clockwise about one of the square's vertices 25 A. B. C. D. Tessa claims that a rotation of 90° clockwise about the center of some polygons will carry the polygon onto itself. Select two polygons that support Tessa's claim. square octagon hexagon rectangle Illuminate Itembank™ Generated On February 8, 2016, 3:59 PM PST 44,579.6 m3 5572.4 m3 1393.1 m3 506.6 m3 Danny is building a pyramid modeled after one of the Great Pyramids of Giza in Egypt. The Great Pyramid has a height of 480 feet and a square base with a side measuring 755 feet. If Danny builds the pyramid to one–eightieth the size, what will the volume be for his pyramid? (Round all numbers to the nearest tenth.) A. B. C. D. 18.8 ft3 176.7 ft3 530.1 ft3 1,140,050 ft3 Continue: Turn to the next page. Page 6 Geometry February Break Extra Credit Assessment ID: ib.573505 Directions: Answer the following question(s). 29 A grain silo is approximately 85% full. A 55 lb sack of grain measures 2 cubic feet. What is the best estimate of the number of bags of grain that can be filled using all the grain in the silo? A. B. C. D. 1708 bags 2010 bags 6833 bags 32 What will be the coordinates of B'? A. B. C. D. A. B. C. D. 31 A. (2 , 3) (2 , 1) (2 , 0) (0 , 2) 8038 bags 33 30 Triangle ABC is reflected over the line y = 1 to produce triangle A'B'C'. Square ABCD is shown below. How many times do parallel lines intersect? 0 1 2 3 Select each statement that is true for all reflections in the coordinate plane. Square ABCD is reflected about side BC. Which of the following statements are true? Select three that apply. A point that is mapped to itself after a reflection is on the line of reflection. B. A line segment connecting a point and its image will be perpendicular to the line of reflection. C. The distance between a point and its image will be twice the distance between the point and the line of reflection. Illuminate Itembank™ Generated On February 8, 2016, 3:59 PM PST A. B. C. D. Vertex B is the midpoint of AA'. Side BC is parallel to AA'. The length of CD is equal to the length of C'D'. Vertex C and vertex C' are located at the same point. Continue: Turn to the next page. Page 7 Geometry February Break Extra Credit Assessment ID: ib.573505 Directions: Answer the following question(s). 34 Anthony draws parallelogram ABCD below and investigates the reflections and rotations that carry it onto itself. 37 After examining the following graph, Kate claims that WXYZ is translated according to the rule (x, y) → (x + 11, y – 2). Is she correct? Anthony claims that a rotation of 360° is the only transformation that carries parallelogram ABCD onto itself. Which of the following transformations could be used to refute Anthony's claim? Select three that apply. A. B. C. D. 35 A reflection over diagonal AC. A reflection over diagonal BD. A rotation of 90° clockwise about its center. A rotation of 180° clockwise about its center. A. Yes, Kate is correct. B. No, WXYZ is translated by the rule (x, y) → (x – 11, y + 2). C. No, WXYZ is translated by the rule (x, y)→ (x + 2, y – 11). A circle is defined as A. a flat surface extending in all directions. B. all points between and including two given points. D. No, WXYZ is translated by the rule (x, y) → (x – 2, y + 11). 38 C. a closed plane figure in which all sides are line 1 segments. D. the set of all points that are a fixed distance from A. B. C. D. On a sunny day, Elliot notices that a lamp post casts a shadow on the ground. If the shadow is 18 ft long and the lamp post is 13 ft tall, what is the angle of elevation of the sun? (Assume the lamp post is at a right angle to the ground.) of its actual size. What would be 10,000,000 a given point. 36 The radius of Earth is 20,903,520 feet. Mark wants to make a model globe of Earth that is the volume of Mark's globe? (Round to the nearest tenth. Use π = 3.14.) A. B. C. D. 8.8 ft3 18.3 ft3 28.7 ft3 38.2 ft3 35.84° 43.76° 46.24° 54.16° Illuminate Itembank™ Generated On February 8, 2016, 3:59 PM PST Continue: Turn to the next page. Page 8 Geometry February Break Extra Credit Assessment ID: ib.573505 Directions: Answer the following question(s). 39 A. B. C. D. What must be the length of PQ in order for ΔJKL to be similar to ΔPQR? 41 Based on the triangles shown below, Theodore claims that ΔTUV is similar to ΔWXY with a scale factor of 3:2. Is Theodore correct? 8 15 18 A. Yes, the triangles are similar with a scale factor of 3:2. 19 B. No, the triangles are similar with a scale factor of 40 Which pair of the following figures is similar? A. 2:1. C. No, the triangles are similar with a scale factor of 2:3. D. No, the triangles are similar with a scale factor of 4:3. B. C. 42 A. B. C. D. 43 D. Illuminate Itembank™ Generated On February 8, 2016, 3:59 PM PST A. B. C. D. A tree is standing next to a 40 foot high building. The tree has an 18 foot shadow, while the building has a 16 foot shadow. How tall is the tree rounded to the nearest foot? 42 feet 36 feet 45 feet 7 feet Which of the following is NOT a valid Triangle Congruence Theorem? SSS ASA SAS SSA Continue: Turn to the next page. Page 9 Geometry February Break Extra Credit Assessment ID: ib.573505 Directions: Answer the following question(s). 44 Mikhail draws triangles ABC and DEF, as shown below, and claims that the two triangles are similar. Select all methods that can be used to justify the claim. A. show that ∠C ≅ ∠D and that all corresponding 45 What is the volume of the right cylinder pictured below? A. 69 π mm3 B. 80 π mm3 C. 150 π mm3 D. 600 π mm3 sides are congruent B. show that ∠C ≅ ∠D and that all corresponding 46 Find the volume of the pyramid and round to the nearest tenth. sides are proportional C. show that a sequence of rotations, reflections, and translations carries triangle ABC onto triangle DEF D. show that a sequence of rotations, reflections, translations, and dilations carries triangle ABC onto triangle DEF A. B. C. D. Illuminate Itembank™ Generated On February 8, 2016, 3:59 PM PST 33.3 cm3 37.5 cm3 66.7 cm3 100 cm3 Continue: Turn to the next page. Page 10 Geometry February Break Extra Credit Assessment ID: ib.573505 Directions: Answer the following question(s). 47 Which theorem or postulate can be used to prove ΔRPQ ≅ ΔRST? 49 A semi–circle with points A and B is shown below. Given R is the midpoint of QT and QT bisects PS at R. When the semi–circle is rotated about the side AB, which of the following three– dimensional figures is created? A. B. C. D. 48 A. B. C. D. SSS SSA SAS A. B. C. D. cone cylinder cube sphere There is not enough information to prove these triangles are congruent. Roberto is driving his car in a race and needs to plan how far he is going to go and how much gas he needs. The race track is in the shape of a triangle. He needs to know the distance of x so he can plan properly. All distances are miles. Find the value of x. Round to the nearest tenth. 2.4 miles 1.79 miles 1.1 miles None of the above Illuminate Itembank™ Generated On February 8, 2016, 3:59 PM PST Continue: Turn to the next page. Page 11 Geometry February Break Extra Credit Assessment ID: ib.573505 Directions: Answer the following question(s). 50 A bowl is shown below. The diameter of the bowl is 5 inches at its opening and 3 inches at its base. The bowl's height is 4 inches. 51 A driveway is shown below with all of the dimensions given in feet. Kellie develops the three models below to estimate the amount of cereal that can be placed in the bowl. Model 1: A half–sphere with a diameter of 5 inches Model 2: A cylinder with a diameter of 3 inches and a height of 4 inches Model 3: A cylinder with a diameter of 5 inches and a height of 4 inches Which statement is true regarding the amount of cereal that can be placed in the bowl? A. Model 1 overestimates the amount of cereal, while Models 2 and 3 underestimate the amount of cereal. The driveway needs to be resurfaced. What is the best estimate of the area of the driveway? A. B. C. D. 52 B. Model 3 overestimates the amount of cereal, cereal, while Model 2 underestimates the amount of cereal. D. Models 1, 2, and 3 all overestimate the amount of cereal. 125π ft2 225π ft2 500π ft2 A lumberyard is asked to cut down a portion of a forest in order to build a new school. Which of the following would be least useful in determining the volume of wood that the lumberyard can expect? while Models 1 and 2 underestimate the amount of cereal. C. Models 1 and 3 overestimate the amount of 100π ft2 A. B. C. D. 53 the average age of the trees in the forest the average number of trees per acre of forest the dimensions of the average tree in the forest the number of acres in the portion of the forest to be cut down A person wants to estimate the number of fish that are in a lake. Which of the following would be least useful in determining the number of fish in a lake? A. B. C. D. Illuminate Itembank™ Generated On February 8, 2016, 3:59 PM PST the average number of fish per square mile the length and width of the lake the depth of the lake the number of fish caught per day Stop: You have finished the assessment. Page 12