Additional Practice Investigation 1 1. Which of these angles are acute, which are obtuse, and which are right? a. b. c. d. e. f. 1
Additional Practice (continued) Investigation 1 2. Use the diagram of the polygon shown below to answer the following questions. B C D A E a. Estimate the measures of each angle. Angle A: Angle B: Angle C Angle D: Angle E: b. Measure each angle. How do the measures compare with your estimates from part (a)? 2
Additional Practice (continued) Investigation 1 3. In the diagram below, the vertical line segment is a diameter of the circle. Use the diagram and what you know about angle relationships to answer the following questions. 5 4 1 2 3 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? 3
Additional Practice (continued) Investigation 1 4. Find each of the angle measures below using an angle ruler or protractor. C D B A T E a. m BTA b. m CTB c. m ETB d. m DTB e. the complement of m ETC f. the supplement of m BTA A B T C D E 4
Additional Practice (continued) Investigation 1 Draw the polygons described. If there is more than one (or no) shape that you can draw, explain how you know that. 5. Draw a triangle SRT. Side SR 3 inches. Side RT 3 inches. m TRS 120. 6. Draw a parallelogram ABCD. m CBA 75 and m BAD 40. 7. Draw a triangle ABC. Side AB 12 centimeters. Side BC 6 centimeters. Side CA 20 centimeters. 8. Draw an isosceles trapezoid JKLM. m JKL 60 and m KLM 120. Side JK 2 inches and side KL 2 inches. 5
Additional Practice: Digital Assessments Investigation 1 9. Jose drew this shape. What is true regarding his shape? Select all that apply. A C 10. Determine each angle measure using an angle measuring tool and the values from the bank. Values may be used more than once. B 95 100 105 110 120 125 130 135 140 180 n The shape is a polygon. n Angle A is acute. n Angle B is acute. n Angle A is complementary to angle B. n Angle B is supplementary to angle C. 11. Write the letter of each angle in the correct box. A B C D E F Acute Angle Obtuse Angle Right Angle 6
Skill: Polygons Investigation 1 1. Tell whether each figure is a polygon. Explain how you know. a. b. c. d. e. f. 7
Skill: Polygons (continued) Investigation 1 2. Tell whether each figure is a polygon. Explain how you know. a. b. c. d. e. f. 8
Skill: Angles Investigation 1 Shapes and Design Estimate the measure of each angle. Then check your answer with an angle ruler or a protractor. 1. 2. 3. 4. 5. 6. Draw an angle for each measure. 7. 165 8. 25 9. 80 10. 112 9
Additional Practice Investigation 2 Answer parts (a) and (b) for each polygon shown in Exercises 1 6. 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. 1. 2. 3. 4. 5. 6. 10
Additional Practice (continued) Investigation 2 7. The shape below is composed of four polygons. a. Describe the four polygons in the shape. b. Can the shape be used to tile a surface? Make a sketch to demonstrate your answer. 11
Additional Practice (continued) Investigation 2 8. An isosceles triangle has two 50 angles. What is the measure of the third angle? Explain how you found your answer. 9. One angle of an isosceles triangle measures 100. What are the measures of the other two angles? Explain your reasoning. 10. Two of the angles of a parallelogram each measure 75. What are the measures of the other two angles? Explain your reasoning. 11. One angle of a parallelogram measures 40 and another angle measures 140. What are the measures of the other two angles? Explain how you found your answer. 12
Additional Practice (continued) Investigation 2 12. Can a parallelogram have two 45 angles and two 75 angles? Why or why not? 13. For each of the shapes below, find the unknown angle measure without using your angle ruler. a. x b. 120 x x 120 135 15 c. d. 75 x 100 110 x x x 13
Additional Practice: Digital Assessments Investigation 2 14. An isosceles triangle has two angles measuring 40. Use the tiles below to write an equation to find the measure of the third angle. 15. Use values from the bank to label the missing angle measures. 48 77 103 107 119 128 138 40 50 180 360 1 2 3 4 5 42 61 16. Which of these objects can be used to tile a surface? Write the letter of each shape in the correct box. A B C D E Can Tile a Surface Cannot Tile a Surface 14
Skill: Angle Sums and Exterior Angles of Polygons Find the measure of each angle labeled x. 1. 2. 3. 51 25 23 x 30 62 x x 121 Investigation 2 4. 5. x 6. 74 50 x x 53 54 54 80 Find the measure of each angle labeled x. 7. 71 48 8. x 149 9. 43 x 54 98 108 x 130 15
Skill: Angle Sums and Exterior Angles of Polygons Investigation 2 Find the measure of angle 1 in each figure. 10. 11. 65 111 1 55 60 30 39 1 12. 13. 1 37 93 36 51 1 75 68 14. 15. 61 79 40 1 1 44 46 16
Additional Practice Investigation 3 1. A quadrilateral has two sides of length 6. The sum of the lengths of the other two sides is 15. Use this information to answer the following questions. a. Suppose the two sides of length 6 are right next to each other. What might the lengths of the other two sides be? Explain your reasoning. b. Suppose the quadrilateral is a rectangle and the two sides of length 6 are opposite each other. What would the lengths of the other two sides have to be? Explain how you found your answer. c. Could the quadrilateral have two sides of length 6, one side of length 13.5, and one side of length 1.5? Explain why or why not. 2. Bob has sketched an equilateral triangle. The sum of the lengths of the sides is 12. What is the length of each side of Bob s triangle? Explain your reasoning. 17
Additional Practice (continued) Investigation 3 3. 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. 4. Use the triangle to answer the following questions. 2.5 5 a. Alex estimates that the unknown side length is about 4.5. How do you think Alex s estimate compares with the actual length? Explain your reasoning. b. Jennifer estimates that the unknown side length is about 8. How do you think Jennifer s estimate compares with the actual length? Explain. c. Use what you have learned about making triangles with polystrips to estimate the length of the unknown side. Explain why you think your estimate is close to the actual length. 18
Additional Practice (continued) Investigation 3 5. The figure below is made up of squares and triangles. Use the design below and what you know about angle relationships to answer the following questions. 2 1 1 3 4 2 4 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. 19
Additional Practice: Digital Assessments Investigation 3 6. In the figure below, two congruent triangles are embedded in squares. Which statements are true? Select all that apply. 7. Two parallel lines are cut by a transversal. Use the values in the bank to label the measure of each missing angle. 2 1 1 3 65 2 15 25 75 95 105 110 65 n Angle 2 measures 65. n Angle 1 measures 65. n The measure of angle 3 is equal to the measure of angle 2. n The measure of angle 1 is equal to the measure of angle 2. n The measure of angle 3 is 70. n The measure of angle 1 is 70. L 1 75 L 2 8. Write the letter of each shape in the appropriate category. Shapes may belong to more than one category. A B C D E F Rotational Symmetry Reflectional Symmetry 20
Skill: Reflectional Symmetry Investigation 3 Tell whether each figure has reflectional symmetry. If it does, draw the line(s) of symmetry. If not, write none. 1. 2. 3. 4. 5. 6. Is there a line of symmetry for each word? If so, draw it. B O X 7. 8. C H I C O 9. 10. T O O T M O M 21
Skill: Rotational Symmetry Investigation 3 Tell whether each figure has rotational symmetry. If it does, tell how many times the figure fits onto itself in one full turn. If not, write no. 1. 2. 3. 4. 5. 6. 7. 8 9. 22
Skill: Angles and Parallel Lines In each diagram below, lines L 1 and L 2 are parallel lines cut by a transversal. Find the measure of each numbered angle. 1. 2. 3. L 1 Investigation 3 L 2 L 1 L 2 95 1 2 3 4 3 2 4 60 1 1 2 3 4 L 1 L 2 4. Use the figure below. Is line L 1 parallel to line L 2? Explain how you could use an angle ruler to support your conjecture. L 1 L 2 1 3 4 2 7 5 6 8 23