Shapes and Designs - Unit Test Review Sheet

Transcription

1 Name: Class: Date: ID: A Shapes and Designs - Unit Test Review Sheet 1. a. Suppose the measure of an angle is 25. What is the measure of its complementary angle? b. Draw the angles to show that you are correct. 2. Draw a parallelogram with two sides of length 5 cm, two sides of length 3 cm, and angles of 50 and 130. Decide whether the given statement is true or false. Give explanations or sketches to support your answers. 3. A quadrilateral with sides 5, 8, 5, 8, in that order, is always a rectangle. 4. a. Is the triangle below a regular polygon? Explain why or why not. b. Could this triangle be used to tile a surface? Explain why or why not. 5. A square has a perimeter of 16.4 centimeters. What is the length of each side? Explain. 6. Use the diagram below and what you know about angle relationships to answer the following questions. a. What is the measure of angle 3? b. The measure of angle 1 is one-fourth of the measure of angle 3. What is the measure of angle 1? c. What is the measure of angle 2? d. The measure of angle 4 is twice the measure of angle 1. What is the measure of angle 4? e. What is the measure of angle 5? 1

2 Name: ID: A 7. Angela has sketched a rectangle. She says that the lengths of the sides of the rectangle add to 26, and the length of one side is 7. What are the length and width of Angela s rectangle? Explain how you found your answer. 8. Use the design below and what you know about angle relationships to answer the following questions. a. If the measure of angle 1 is 25, what is the measure of angle 2? Explain your reasoning. b. If the measure of angle 1 is 25, what is the measure of angle 3? Explain your reasoning. c. If the measure of angle 1 is 25, what is the measure of angle 4? Explain your reasoning. 9. Is a triangle with angle measures 46, 35, and 100 possible? Explain why or why not. 10. a. Suppose two angles are supplementary and one of them measures 31. What is the measure of the other angle? b. Draw the angles to show that you are correct. Use a coordinate grid like the one shown below. 11. If a line segment connecting (4, 6) and (7, 6) forms one side of a square, what might be the coordinates of the other corners of the square? 2

3 Name: ID: A One of the most common places we see angles is on the faces of clocks. At the start of each hour, the minute hand is pointed straight up, at the 12. On the clocks below, mark where the minute hand is at the start of an hour as one side of an angle. Sketch the angle formed by the minute hand at the time shown, and give the measure of the angle minutes angle = minutes angle = 14. For parts (a) (b), show all the line symmetries and give the degree measures for all the turn symmetries for the given shape. a. b. 3

4 Name: ID: A 15. Polygon ABCD is a rectangle and the lengths of AD and DE are equal. What is the measure of angle BAE? A. 90 B. 40 C. 45 D The figure below is a regular pentagon. Which expression represents the perimeter (distance around) the pentagon? A. 5 s B. s + 5 C. s + s + s + s D. s s 17. Which figure below is a polygon? A. Figure A B. Figure B C. Figure C D. Figure D 4

5 Name: ID: A 18. In which figure is angle DEF less than 90? A. Figure 1 B. Figure 2 C. Figure 3 D. Figure Which of these drawings shows AB parallel to CD and CD perpendicular to EF? A. Figure 5 B. Figure 6 C. Figure 7 D. Figure Name the polygon below. A. quadrilateral B. hexagon C. pentagon D. octagon 5

6 Name: ID: A 21. Which is not a name for this polygon? A. quadrilateral B. parallelogram C. rectangle D. rhombus 22. What is the measure of the angle labeled x? A. 65 B. 90 C. 255 D Identify the polygon by the number of sides. A. quadrilateral B. pentagon C. octagon D. hexagon 24. Name a polygon with 5 sides. A. octagon B. triangle C. pentagon D. hexagon 25. How many lines of symmetry does the figure have? A. 3 B. 4 C. 2 D. 1 6

7 Name: ID: A 26. Which angle measures 117? A. C. B. D. 27. In the diagram, p q. Find the measure of each numbered angle. A. m 1 = m 2 = m 5 = 50 m 3 = m 4 = m 6 = m 7 = 130 B. m 1 = m 2 = m 5 = 130 m 3 = m 4 = m 6 = m 7 =50 C. m 1 = m 2 = m 5 = 120 m 3 = m 4 = m 6 = m 7 = 50 D. m 1 = m 2 = m 5 = 130 m 3 = m 4 = m 6 = m 7 = 45 7

8 Name: ID: A 28. If a and b are parallel lines and m 4 = 45, what is the measure of 7? A. 131 B. 47 C. 135 D Find the sum of the measures of the interior angles of a pentagon. A. 720 B. 900 C. 360 D Find the sum of the measures of the interior angles of a polygon with 12 sides. A. 1,980 B. 1,800 C. 1,620 D. 2, For a regular pentagon, find the sum of the measures of the angles. Then find the measure of each angle. If necessary, round your answer to the nearest degree. A. 360 ; 120 B. 540 ; 270 C. 720 ; 140 D. 540 ; Find the measure of each angle of a regular polygon with 5 sides. A. 180 B. 216 C. 120 D

9 ID: A Shapes and Designs - Unit Test Review Sheet Answer Section 1. ANS: a. 65, because if two angles are complementary, then their sum is 90, so = 65. b. PTS: 1 DIF: L2 REF: Shapes and Designs Unit Test TOP: Problem 1.4 KEY: parallel lines transversal exterior angle 2. ANS: Possible answers: PTS: 1 DIF: L2 REF: Shapes and Designs Unit Test OBJ: Investigation 3: Designing Triangles and Quadrilaterals NAT: CC 7.EE.B.4 CC 7.G.A.2 CC 7.G.B.5 NAEP G1b NAEP G1c NAEP G1d NAEP G2a NAEP G2d TOP: Problem 3.3 KEY: reflection symmetry line of symmetry rotation symmetry 3. ANS: False; it could be a rectangle or it could be just a parallelogram. Thus the always part of the statement is not true. PTS: 1 DIF: L2 REF: Shapes and Designs Extra Questions OBJ: Investigation 3: Designing Triangles and Quadrilaterals NAT: CC 7.EE.B.4 CC 7.G.A.2 CC 7.G.B.5 NAEP G1d TOP: Problem 4.2 Building Quadrilaterals KEY: side lengths of quadrilaterals quadrilateral parallelogram 1

10 ID: A 4. ANS: a. No, because all sides and angles of the triangle are not equal. b. Yes; any triangle can be used to tile the plane. PTS: 1 DIF: L2 REF: Shapes and Designs Extra Questions NAT: CC 7.EE.A.2 CC 7.EE.B.4 CC 7.G.A.2 CC 7.G.B.5 NAEP A1a NAEP G1d NAEP G2d NAEP G3c NAEP G3f TOP: Problem 3.3 Interior Angles in Tilings KEY: tiling triangle regular polygon 5. ANS: Each side would have length 16.4 = PTS: 1 DIF: L2 REF: Shapes and Designs Extra Questions OBJ: Investigation 3: Designing Triangles and Quadrilaterals NAT: CC 7.EE.B.4 CC 7.G.A.2 CC 7.G.B.5 NAEP G1d TOP: Problem 4.2 Building Quadrilaterals KEY: perimeter square side lengths of quadrilaterals 6. ANS: a. 90 b c d. 45 e. 135 PTS: 1 DIF: L2 REF: Shapes and Designs Additional Practice Investigation 2 KEY: ray vertex degrees right angle 7. ANS: One pair of sides would have length 7, and the other pair would have length 6. PTS: 1 DIF: L2 REF: Shapes and Designs Additional Practice Investigation 4 OBJ: Investigation 3: Designing Triangles and Quadrilaterals NAT: CC 7.EE.B.4 CC 7.G.A.2 CC 7.G.B.5 NAEP G1d KEY: rectangle side lengths of quadrilaterals 8. ANS: a. 40 ; 90 2(25 ) = = 40. b. 65 ; 180 ( ) = = 65. c. 70 ; since the sum of measures of angle 4 and angle 2 is 180 (they are the interior angles of a triangle) and since angle 2 is 40 [from part (a)], twice the measure of angle 4 is = 140. So angle 4 is 70. PTS: 1 DIF: L2 REF: Shapes and Designs Additional Practice Investigation 4 OBJ: Investigation 3: Designing Triangles and Quadrilaterals NAT: CC 7.EE.B.4 CC 7.G.A.2 CC 7.G.B.5 NAEP G1d TOP: Problem 4.2 Building Quadrilaterals KEY: angle sums angles 2

11 ID: A 9. ANS: No; the sum of the angles is = 181. A triangle has an angle sum of exactly 180. PTS: 1 DIF: L2 REF: Shapes and Designs Unit Test NAT: CC 7.EE.A.2 CC 7.EE.B.4 CC 7.G.A.2 CC 7.G.B.5 NAEP A1a NAEP A2c NAEP G1d NAEP G2d NAEP G3c NAEP G3f NAEP G3g NAEP M1c NAEP M1g NAEP M2e TOP: Problem 2.2 KEY: ray vertex degrees right angle angle sum 10. ANS: a. 149, because if two angles are supplementary, then their sum is 180, so = 147. b. PTS: 1 DIF: L2 REF: Shapes and Designs Unit Test TOP: Problem 1.4 KEY: reflection symmetry line of symmetry rotation symmetry 11. ANS: One possibility is (4, 3) and (7, 3); the other is (4, 9) and (7, 9). PTS: 1 DIF: L2 REF: Shapes and Designs Extra Questions TOP: Problem 2.2 Developing Angle Benchmarks KEY: angle benchmarks line segment 12. ANS: angle = 270 PTS: 1 DIF: L2 REF: Shapes and Designs Extra Questions TOP: Problem 2.1 Understanding Angles KEY: ray vertex degrees right angle 3

12 ID: A 13. ANS: angle = 150 PTS: 1 DIF: L2 REF: Shapes and Designs Extra Questions TOP: Problem 2.1 Understanding Angles KEY: ray vertex degrees right angle 14. ANS: a. The pentagon has five lines of symmetry, the lines connecting each vertex to the midpoint of the opposite side. The regular pentagon also has five turn symmetries: 72, 144, 216, 288, and 360. b. The rhombus has two lines of symmetry, the two diagonals of the shape. There are also two turn symmetries: 180 and 360. PTS: 1 DIF: L2 REF: Shapes and Designs Extra Questions TOP: Problem 1.2 Symmetry KEY: reflection symmetry line of symmetry rotation symmetry 15. ANS: C PTS: 1 DIF: L2 NAT: CC 7.EE.A.2 CC 7.EE.B.4 CC 7.G.A.2 CC 7.G.B.5 NAEP A1a NAEP G1d NAEP G2d NAEP G3c NAEP G3f TOP: Problem 3.2 Angle Sums of Any Polygon KEY: polygon angle measures angle sums right angle 4

13 ID: A 16. ANS: A PTS: 1 DIF: L2 OBJ: Investigation 3: Designing Triangles and Quadrilaterals NAT: CC 7.EE.B.4 CC 7.G.A.2 CC 7.G.B.5 NAEP G1d TOP: Problem 4.2 Building Quadrilaterals KEY: regular pentagon perimeter 17. ANS: D PTS: 1 DIF: L2 TOP: Problem 1.1 Classifying Polygons KEY: polygon vertex line segment equilateral triangle isosceles triangle scalene triangle rectangle square parallelogram 18. ANS: D PTS: 1 DIF: L2 TOP: Problem 2.1 Understanding Angles KEY: ray vertex degrees right angle 19. ANS: C PTS: 1 DIF: L2 TOP: Problem 2.5 Angles and Parallel Lines KEY: parallel lines transversal 20. ANS: B PTS: 1 DIF: L2 TOP: Problem 1.1 Classifying Polygons KEY: polygon vertex line segment equilateral triangle isosceles triangle scalene triangle rectangle square parallelogram 21. ANS: D PTS: 1 DIF: L2 TOP: Problem 1.1 Classifying Polygons KEY: polygon vertex line segment equilateral triangle isosceles triangle scalene triangle rectangle square parallelogram 22. ANS: D PTS: 1 DIF: L2 NAT: CC 7.EE.A.2 CC 7.EE.B.4 CC 7.G.A.2 CC 7.G.B.5 NAEP A1a NAEP G1d NAEP G2d NAEP G3c NAEP G3f TOP: Problem 3.1 Angle Sums of Regular Polygons KEY: angle sum 23. ANS: A PTS: 1 DIF: L1 REF: Skills Practice Investigation 1 TOP: Problem 1.1 Classifying Polygons KEY: pentagon octagon quadrilateral hexagon polygon 5

14 ID: A 24. ANS: C PTS: 1 DIF: L1 REF: Skills Practice Investigation 1 TOP: Problem 1.1 Classifying Polygons KEY: pentagon octagon quadrilateral hexagon triangle decagon polygon 25. ANS: C PTS: 1 DIF: L1 REF: Skills Practice Investigation 1 TOP: Problem 1.2 Symmetry KEY: line symmetry line of symmetry symmetry 26. ANS: D PTS: 1 DIF: L1 REF: Skills Practice Investigation 2 TOP: Problem 2.1 Understanding Angles Problem 2.2 Developing Angle Benchmarks Problem 2.3 Measuring Angles KEY: angle protractor 27. ANS: B PTS: 1 DIF: L1 REF: Skills Practice Investigation 2 TOP: Problem 2.5 Angles and Parallel Lines KEY: alternate interior angles corresponding angles 28. ANS: C PTS: 1 DIF: L2 REF: Skills Practice Investigation 2 TOP: Problem 2.5 Angles and Parallel Lines KEY: alternate interior angles corresponding angles 29. ANS: D PTS: 1 DIF: L1 REF: Skills Practice Investigation 3 NAT: CC 7.EE.A.2 CC 7.EE.B.4 CC 7.G.A.2 CC 7.G.B.5 NAEP A1a NAEP G1d NAEP G2d NAEP G3c NAEP G3f TOP: Problem 3.2 Angle Sums of Any Polygon KEY: polygon angle sum 30. ANS: B PTS: 1 DIF: L1 REF: Skills Practice Investigation 3 NAT: CC 7.EE.A.2 CC 7.EE.B.4 CC 7.G.A.2 CC 7.G.B.5 NAEP A1a NAEP G1d NAEP G2d NAEP G3c NAEP G3f TOP: Problem 3.2 Angle Sums of Any Polygon KEY: polygon angle sum 31. ANS: D PTS: 1 DIF: L2 REF: Skills Practice Investigation 3 NAT: CC 7.EE.A.2 CC 7.EE.B.4 CC 7.G.A.2 CC 7.G.B.5 NAEP A1a NAEP G1d NAEP G2d NAEP G3c NAEP G3f TOP: Problem 3.2 Angle Sums of Any Polygon KEY: polygon angle sum regular polygon angle measures of a polygon 32. ANS: D PTS: 1 DIF: L1 REF: Skills Practice Investigation 3 NAT: CC 7.EE.A.2 CC 7.EE.B.4 CC 7.G.A.2 CC 7.G.B.5 NAEP A1a NAEP G1d NAEP G2d NAEP G3c NAEP G3f TOP: Problem 3.2 Angle Sums of Any Polygon KEY: polygon angle sum regular polygon angle measures of a polygon 6