examview - shapes and designs unit test...

Name: ________________________ Class: ___________________ Date: __________ ID: A

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Shapes and Designs Unit Test - Each question is worth 2 points.

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

____ 1. Name the polygon below.

a. quadrilateral b. hexagon c. pentagon d. octagon

____ 2. Which of these drawings shows AB parallel to CD and CD perpendicular to EF?

a. Figure A b. Figure B c. Figure C d. Figure D

____ 3. The measures of two angles of a triangle are 42 and 89. Find the measure of the third angle.

a. 131 b. 49 c. 47 d. 41

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Name: ________________________ ID: A

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____ 4. Which of the following angles has a measure of 160°?a. c.

b. d.

____ 5. If a and b are parallel lines and m3 = 141º, what is the measure of 8?

a. 39º b. 146º c. 43º d. 36º




Name: ________________________ ID: A

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____ 6. Find the value of x in the triangle.

a. 289 b. 71 c. 27 d. 109

____ 7. Find the sum of the measures of the angles of the figure.

a. 720 b. 540 c. 1260 d. 900

____ 8. Polygon ABCD is a rectangle and the lengths of AD and DE are equal. What is the measure of angle BAE?

a. 90º b. 40º c. 45º d. 100º




Name: ________________________ ID: A

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Short Answer

9. An isosceles triangle has two 50º angles. What is the measure of the third angle? Explain how you found your answer.

.

Decide whether the given statements are true or false. Give explanations or sketches to support your answers.

10. All rectangles are special kinds of parallelograms.

.

11. All parallelograms are special kinds of squares.

.

12. You can always completely surround a point by placing the vertices of four squares together.

.




Name: ________________________ ID: A

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13. 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.

Without using an angle ruler, find the measure of the following angle.

.

For questions 14 and 15, use the coordinate grids given below to answer the questions.

14. 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?

.

15. If (2, 0) and (5, 5) are two vertices of a triangle that does not have a right angle, what might be the coordinates of the other vertex of the triangle?

.




Name: ________________________ ID: A

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16. In the diagram, line L1 is parallel to line L2.

a. What is the measure of 3? Explain how you found your answer.

b. What is the measure of 1? Explain how you found your answer.

.

Use an angle ruler to measure each angle.

17.

.

18.




Name: ________________________ ID: A

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Use the given data and what you know about relations among sides and angles to find the lengths and angle measurements of all sides and angles in the figure.

19. square

.

20. parallelogram

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21. 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.




Name: ________________________ ID: A

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22. An equilateral triangle has a perimeter of 12. What is the length of each side? Explain.

.

Answer parts (a) and (b) for each polygon.a. Is the shape a regular polygon? Explain why or why not.b. Could the shape be used to tile a surface? Make a sketch to demonstrate your answer.

23.

.

24.

.

25. Use the design below and what you know about angle relationships to answer the following questions.

a. If the measure of angle 1 is 25º, what is the measure of angle 2? Explain your reasoning.

b. If the measure of angle 1 is 25º, what is the measure of angle 3? Explain your reasoning.

c. If the measure of angle 1 is 25º, what is the measure of angle 4? Explain your reasoning.




Name: ________________________ ID: A

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26. EXTRA CREDIT:

Below is the face of a compass. It is standard practice to match each compass direction with the degree measure of the angle formed by a clockwise turn from due north (N) to the desired direction. For example, east (E) is given the direction number 90º.

For parts (a) – (h), find the direction number for the given point of the compass.

________ a. NE (northeast) ________ b. SE (southeast)________ c. S (south) ________ d. SW (southwest)________ e. W (west) ________ f. NW (northwest)________ g. N (north) ________ h. NNE (north-northeast, between N and NE)

.

27. How many sides does a regular polygon have if each exterior angle measures 30?




ID: A

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SHORT ANSWER

9. ANS: Since the sum of the angles must be 180º, the third angle must have a measure of 80º.

PTS: 2 DIF: L2 REF: Shapes and Designs | Additional Practice Investigation 3OBJ: Investigation 3: Polygon Properties and Tiling NAT: NAEP G1d| NAEP G2d| NAEP G3c| NAEP G3f| NAEP A1a TOP: Problem 3.1 Angle Sums of Regular Polygons KEY: angle sum

10. ANS: True; to be a parallelogram, a figure must have four sides, with opposite sides equal and opposite angles equal. A rectangle meets these requirements and has the additional requirement that all four of its angles are 90°.

PTS: 2 DIF: L2 REF: Shapes and Designs | Extra QuestionsOBJ: Investigation 1: Bees and Polygons NAT: NAEP G1b| NAEP G1c| NAEP G1d| NAEP G2a| NAEP G2d TOP: Problem 1.1 Classifying Polygons KEY: polygon | vertex | line segment | equilateral triangle | isosceles triangle | scalene triangle | rectangle | square | parallelogram

11. ANS: False; not every parallelogram has four equal sides, or four right angles. However, a square is a special parallelogram.

PTS: 2 DIF: L2 REF: Shapes and Designs | Extra QuestionsOBJ: Investigation 1: Bees and Polygons NAT: NAEP G1b| NAEP G1c| NAEP G1d| NAEP G2a| NAEP G2d TOP: Problem 1.1 Classifying Polygons KEY: polygon | vertex | line segment | rectangle | square | parallelogram

12. ANS: True; the angles that fit around a single point must add to 360º. Because a square has 90º angles and the sum of four 90º angles is 360º, this will work.

PTS: 2 DIF: L2 REF: Shapes and Designs | Extra QuestionsOBJ: Investigation 1: Bees and Polygons NAT: NAEP G1b| NAEP G1c| NAEP G1d| NAEP G2a| NAEP G2d TOP: Problem 1.3 Tiling With Regular Polygons KEY: regular polygon | tiling

13. ANS: 60°

PTS: 2 DIF: L2 REF: Shapes and Designs | Check-UpOBJ: Investigation 2: Polygons and Angles NAT: NAEP M1c| NAEP M1g| NAEP M2e| NAEP G3g| NAEP A2c TOP: Problem 2.1 Understanding Angles | Problem 2.3 Measuring AnglesKEY: ray | vertex | degrees | right angle




ID: A

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14. ANS: One possibility is (4, 3) and (7, 3); the other is (4, 9) and (7, 9).

PTS: 2 DIF: L2 REF: Shapes and Designs | Extra QuestionsOBJ: Investigation 2: Polygons and Angles NAT: NAEP M1c| NAEP M1g| NAEP M2e| NAEP G3g| NAEP A2c TOP: Problem 2.2 Developing Angle Benchmarks KEY: angle | benchmarks | line segment

15. ANS: Possible answer: (0, 5). Note: (5, 0) and (2, 5) will give right triangles and thus are incorrect. Make sure that two sides are greater than the third side in order for the figure to be a triangle.

PTS: 2 DIF: L2 REF: Shapes and Designs | Extra QuestionsOBJ: Investigation 2: Polygons and Angles NAT: NAEP M1c| NAEP M1g| NAEP M2e| NAEP G3g| NAEP A2c TOP: Problem 2.2 Developing Angle Benchmarks KEY: angle | benchmarks | vertices | line segment

16. ANS: Answers will vary. Some students may measure with an angle ruler, and others may apply what they know about supplementary angles to find that m3 = 110º, and then use what they know about alternate interior angles to conclude that m1 = 110º.

PTS: 2 DIF: L2 REF: Shapes and Designs | Extra QuestionsOBJ: Investigation 2: Polygons and Angles NAT: NAEP M1c| NAEP M1g| NAEP M2e| NAEP G3g| NAEP A2c TOP: Problem 2.5 Angles and Parallel Lines KEY: parallel lines | transversal

17. ANS: about 20º

PTS: 2 DIF: L2 REF: Shapes and Designs | Extra QuestionsOBJ: Investigation 2: Polygons and Angles NAT: NAEP M1c| NAEP M1g| NAEP M2e| NAEP G3g| NAEP A2c TOP: Problem 2.3 Measuring Angles KEY: angle | measuring angles | angle ruler

18. ANS: about 125º

PTS: 2 DIF: L2 REF: Shapes and Designs | Extra QuestionsOBJ: Investigation 2: Polygons and Angles NAT: NAEP M1c| NAEP M1g| NAEP M2e| NAEP G3g| NAEP A2c TOP: Problem 2.3 Measuring Angles KEY: angles | measuring angles | angle ruler

19. ANS: All sides are 2 cm and all angles are 90º.

PTS: 2 DIF: L2 REF: Shapes and Designs | Extra QuestionsOBJ: Investigation 3: Polygon Properties and Tiling NAT: NAEP G1d| NAEP G2d| NAEP G3c| NAEP G3f| NAEP A1a TOP: Problem 3.2 Angle Sums of Any Polygon KEY: angle sum | side lengths of quadrilaterals




ID: A

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20. ANS: Opposite sides must be of equal length, so the short side is 2 cm, and the long side is 4 cm. Opposite angles

must be equal, so the other obtuse angle is 120º. The two acute angles are equal, and each must be 360 240

2

= 60º.

PTS: 2 DIF: L2 REF: Shapes and Designs | Extra QuestionsOBJ: Investigation 3: Polygon Properties and Tiling NAT: NAEP G1d| NAEP G2d| NAEP G3c| NAEP G3f| NAEP A1a TOP: Problem 3.2 Angle Sums of Any Polygon KEY: parallelogram | side lengths | obtuse angle | acute angle

21. 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: 72º, 144º, 216º, 288º, and 360º.b. The rhombus has two lines of symmetry, the two diagonals of the shape. There are also two turn symmetries:

180º and 360º.

PTS: 2 DIF: L2 REF: Shapes and Designs | Extra QuestionsOBJ: Investigation 1: Bees and Polygons NAT: NAEP G1b| NAEP G1c| NAEP G1d| NAEP G2a| NAEP G2d TOP: Problem 1.2 Symmetry KEY: reflection symmetry | line of symmetry | rotation symmetry

22. ANS:

Each side would have a length 123

= 4.

PTS: 2 DIF: L2 REF: Shapes and Designs | Extra QuestionsOBJ: Investigation 4: Building Polygons NAT: NAEP G1d TOP: Problem 4.1 Building TrianglesKEY: side lengths of triangles | triangle | perimeter




ID: A

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23. ANS: a. The shape is not a regular polygon because it does not contain sides and angles that are all the same size.b. The shape can be used to tile a surface. Drawings will vary.

PTS: 2 DIF: L2 REF: Shapes and Designs | Additional Practice Investigation 1OBJ: Investigation 1: Bees and Polygons NAT: NAEP G1b| NAEP G1c| NAEP G1d| NAEP G2a| NAEP G2d TOP: Problem 1.1 Classifying Polygons | Problem 1.3 Tiling With Regular PolygonsKEY: polygon | vertex | line segment | equilateral triangle | isosceles triangle | scalene triangle | rectangle | square | parallelogram | regular polygon | tiling

24. ANS: a. The shape is not a regular polygon because it does not contain sides and angles that are all the same size.b. The shape cannot be used to tile a surface. Drawings will vary.


25. ANS: a. 40º; 90º– 2(25º) = 90º– 50º = 40º.b. 65º; 180º– (90º + 25º) = 180º– 115º = 65º.c. 70º; since the sum of measures of angle 4 and angle 2 is 180º (they are the interior angles of a triangle) and

since angle 2 is 40º [from part (a)], twice the measure of angle 4 is 180º – 40º = 140º. So angle 4 is 70º.

PTS: 2 DIF: L2 REF: Shapes and Designs | Additional Practice Investigation 4OBJ: Investigation 4: Building Polygons NAT: NAEP G1d TOP: Problem 4.2 Building QuadrilateralsKEY: angle sums | angles

26. ANS: a. 45º b. 135ºc. 180º d. 225ºe. 270º f. 315ºg. 0º h. 22.5º

PTS: 2 DIF: L2 REF: Shapes and Designs | Extra QuestionsOBJ: Investigation 2: Polygons and Angles NAT: NAEP M1c| NAEP M1g| NAEP M2e| NAEP G3g| NAEP A2c TOP: Problem 2.2 Developing Angle Benchmarks KEY: angle benchmarks | measuring angles




ID: A

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27. ANS: 12 sides

PTS: 2 DIF: L1 REF: Skills Practice Investigation 3OBJ: Investigation 3: Polygon Properties and Tiling NAT: NAEP G1d| NAEP G2d| NAEP G3c| NAEP G3f| NAEP A1a TOP: Problem 3.4 Exterior Angles of Polygons KEY: sum of angles of a polygon | exterior angle




ID: A Shapes and Designs Unit Test - Each question is worth 2 points. [Answer Strip]

_____ 1.B

_____ 2.D

_____ 3.B

_____ 4.D

_____ 5.A

_____ 6.B

_____ 7.B

_____ 8.C




Name: ________________________ Class: ___________________ Date: __________ ID: A

1

Shapes and Designs Unit Test - Each question is worth 2 points.

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

____ 1. Name the polygon below.

a. quadrilateral b. hexagon c. pentagon d. octagon

____ 2. Which of these drawings shows AB parallel to CD and CD perpendicular to EF?

a. Figure A b. Figure B c. Figure C d. Figure D

____ 3. The measures of two angles of a triangle are 42 and 89. Find the measure of the third angle.

a. 131 b. 49 c. 47 d. 41


