Name. STAR CITY Math / Geometry / Review Packet for Teacher Period

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1 STAR CITY Math / Geometry / Review Packet for Quincy, Rita, Sheila, and Theo all parked their cars next to each other in the school parking lot. The cars each have a different color: blue, green, red, and white. Name Teacher Period 2. The figure below is a Venn diagram representing 100 pizzas and the percentage sold with 3 different types of meat toppings. The blue car is between Quincy s car and the green car. Rita parked her car next to the green car. Theo owns the red car which is parked next to Sheila s car. Based on the statements above, who has the blue car? A. Quincy B. Rita C. Sheila D. Theo What percentage of pizzas do not have pepperoni, ham, or sausage as a topping? A. 9 B. 13 C. 18 D. 31 1

2 Use the figure below to answer question 3. STAR CITY Math Geometry Review Packet for Given: GL NE, Which statement/reason pair would not be included in proving 2 3? A. 2 5 because if two parallel lines are cut by a transversal, corresponding angles are congruent. B. 3 6 because if two parallel lines are cut by a transversal, alternate interior angles are congruent. C. 4 2 because vertical angles are congruent. D. 2 3 because congruence of angles is transitive. 2

3 4. Demetria graphs circle C, shown below. STAR CITY Math Geometry Review Packet for Next, Demetria plans to reflect circle C across the y-axis, then translate the image down by 3 units. What will be the new coordinates of the center of circle C? A. ( 4, 1) B. ( 4, 2) C. (4, 5) D. (4, 1) 3

4 5. What is the value of x that makes l m? STAR CITY Math Geometry Review Packet for A. 0 B. 15 C. 30 D In the figure below, which would prove x y? A. m 1 = 60 B. m 2 = 60 C. m 3 = 120 D. m 5 = 120 4

5 STAR CITY Math Geometry Review Packet for Avari is making a quilt using the Arkansas Traveler Variation pattern. She starts with the block below. To draw the pattern, Avari sketches a second block by rotating the first block 90-degrees clockwise about the origin. Avari sketches two more blocks, each time rotating the previous block 90-degrees clockwise about the origin. When she completes the four blocks, which pattern has Avari made? A. B. C. D. 5

6 STAR CITY Math Geometry Review Packet for Which would be sufficient to prove JK LM? 10. Which is sufficient to prove that lines m and n are parallel? A. m 2 = m 3 B. m 2 = m 4 C. m 1 + m 3 = 90 D. m 2 + m 3 = Two parallel lines, m and n, are cut by a transversal, t, as shown in the diagram below. A. m 3 = m 6 B. m 5 = m 8 C. m 3 + m 4 = 180 D. m 4 + m 2 = 180 Which angles are congruent to 1? A. 5 only B. 4 only C. 4 and 5 only D. 4, 5, and 8 6

7 Use the figure below to answer question 11. STAR CITY Math Geometry Review Packet for The pythagorean theorem can be proved given ΔXYZ, YZX is a right angle, and m is an altitude as shown in the proof below. Statement 1. ΔXYZ ΔXZW ΔZYW 2. c a = a k, c b = b j Reasons 1. altitude to the hypotenuse forms two right triangles that are similar to each other and to the original triangle. 2. corresponding parts of similar triangles are proportional 3. ck = a 2, cj = b 2 3. cross products are equal 4. ck + cj = a 2 + b 2 4. addition property of equality 5. c(k + j) = a 2 + b 2 5. distributive property 6. c = k + j 6.? 7. c(c) = a 2 + b 2 7. substitution 8. c 2 = a 2 + b 2 8. definition of c 2 What is the reason for statement 6? A. segment addition postulate B. geometry mean theorem C. triangle equality theorem D. definition of division 7

8 12. Alice, Bob, Colleen, and Dave are in line at a grocery store. Each needs to buy a different item. The items are bread, cereal, milk, and fruit. STAR CITY Math Geometry Review Packet for Bob was second in line, after the person who bought milk but before the person who bought the bread. 2. Colleen did not buy the fruit. 3. Alice bought the cereal. 4. Dave was the first person in line. Based on the statements, who bought the loaf of bread? A. Alice B. Bob C. Colleen D. Dave 8

9 13. Given: ΔXYZ and XZ YR Prove: m 1 + m 2 + m 3 = 180 STAR CITY Math Geometry Review Packet for What is the reason in Step 2? A. Vertical angles are congruent. B. Complementary angles are congruent. C. Corresponding angles of parallel lines are congruent. D. Alternate interior angles of parallel lines are congruent. 9

10 STAR CITY Math Geometry Review Packet for Use the figure below to answer question The figure below is translated 3 units to the right, then 5 units down, and finally reflected over the x-axis. 14. Donna describes the piece of artwork shown above. Which is the most accurate description of this artwork? A. One shape reflects and translates onto the other. B. One shape rotates onto the other. C. One shape reflects onto the other. D. One shape rotates and translates onto the other. 15. In the figure below, m n. What are the coordinates of the image of point X after the transformations? A. (í 2, í 2) B. (í 2, 2) C. (2, í 2) D. (2, 2) What is the value of x? A. 36 B. 72 C. 108 D

11 17. Todd, Bill, and Jeff play 1 st, 2 nd, and 3 rd base at the University of Arkansas at Monticello, but not necessarily in that order. STAR CITY Math Geometry Review Packet for Todd does not play 2 nd base. Bill is majoring in business. The 1 st baseman lives in the dorm. The 3 rd baseman is majoring in communications. Todd and Bill share an apartment. Which of the following correctly pairs each player with his position? A. Todd 1 st base, Bill 2 nd base, Jeff 3 rd base B. Todd 3 rd base, Bill 2 nd base, Jeff 1 st base C. Todd 1 st base, Bill 3 rd base, Jeff 2 nd base D. Todd 3 rd base, Bill 1 st base, Jeff 2 nd base 11

12 STAR CITY Math Geometry Review Packet for The figure graphed below is rotated 90 clockwise about the origin and translated up 1 unit. What is the resulting image? A. B. C. D. 12

13 STAR CITY Math Geometry Review Packet for Use the figure below to answer question The table below shows the new coordinates of point (a, b) when it is rotated, counterclockwise about the origin a certain number of degrees. Using this information, what are the new coordinates of (3, 6) when it is rotated 540 about the origin? 19. Main Street and Monroe Street are parallel. Washington Avenue will be built as a straight street intersecting both streets. It will form a 32 angle with Monroe Street shown in the figure above. What will be the measure of 1? A. 32 A. ( 6, 3) B. ( 6, 3) C. (3, 6) D. ( 3, 6) B. 58 C. 122 D

14 STAR CITY Open-Response / Geometry / Review Packet for Name Teacher Period GEOMETRY OPEN-RESPONSE ITEM A A. At Eastview High School, 257 students borrowed materials from the library. 111 students borrowed CDs 15 students borrowed only CDs 47 students borrowed magazines and CDs, but no books 21 students borrowed CDs, magazines, and books 27 students borrowed materials other than books, magazines, and CDs 73 students borrowed books and magazines 137 students borrowed books Copy the Venn diagram above into your Student Answer Document. Complete the diagram by placing the correct number of students in the proper regions. Show or explain all of your work even if you use mental math or a calculator. 14

15 STAR CITY Student Answer Document / Geometry / Review Packet for Name Teacher Period A 15

16 GEOMETRY OPEN-RESPONSE ITEM A (LG.1.G.1C) A. At Eastview High School, 257 students borrowed materials from the library. 111 students borrowed CDs 15 students borrowed only CDs 47 students borrowed magazines and CDs, but no books 21 students borrowed CDs, magazines, and books 27 students borrowed materials other than books, magazines, and CDs 73 students borrowed books and magazines 137 students borrowed books Copy the Venn diagram above into your Student Answer Document. Complete the diagram by placing the correct number of students in the proper regions. Show or explain all of your work even if you use mental math or a calculator.

17 Score RUBRIC FOR GEOMETRY OPEN-RESPONSE ITEM A (LG.1.G.1C) Description 4 All correct values correctly placed on the diagram with all work shown. 3 All correct values correctly placed on the diagram with some work shown. OR The student correctly places 6 or 7 correct values on the diagram with correct work shown for at least 2 of the values. 2 The student correctly places 4 8 correct values on the diagram with no work shown. 1 The student correctly places 2 or 3 correct values on the diagram, with or without work shown. OR The response demonstrates minimal understanding of solving problems using Venn diagrams (i.e., the student shows correct procedure for determining at least one of the values other than the given values, which may or may not be placed on the diagram.) 0 No understanding. Work is either incorrect or irrelevant. B No response. Note: Correct answers will include values obtained by error(s) carried through (e.g., if the student uses 73 for Books AND Magazines ONLY, then the correct value for Books only will be 15. In this case, 15 is considered correct based on a previous error carried through).

18 Solution and Scoring Sample Solution: Given Values: CD s Only: 15 Magazines and CD s, no books: 47 Materials other than books, magazines, and CD s: 27 Magazines, CD s and books: 21 Other Values (Values that need to be determined): CD s and books only: 111 ( ) = 28 Books and magazines only: = 52 Books only: 137 ( ) = 36 Magazines only: 257 ( ) = 31

19 STAR CITY Math / Geometry / Review Packet for Answer Key and Alignment Answer Source SLE 1. B AR LG.1.G.1c 2. A AR LG.1.G.1c 3. C TLI LG.1.G.6 4. A AR CGT.5.G.7c 5. C AR LG.1.G.5a 6. B AR LG.1.G.5a 7. A AR CGT.5.G.7c 8. A AR LG.1.G.5a 9. D AR LG.1.G.5a 10. A AR LG.1.G.5a 11. A TLI LG.1.G C AR LG.1.G.1c 13. C AR LG.1.G A AR CGT.5.G.7c 15. A AR LG.1.G.5a 16. B AR CGT.5.G.7c 17. B AR LG.1.G.1c 18. D AR CGT.5.G.7c 19. A AR LG.1.G.5a 20. D AR CGT.5.G.7a