1ACE Exercise 6. Name Date Class. 6. a. Draw ALL the lines of symmetry on Shape 1 and Shape 2 below. HINT Refer back to Problem 1.

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1 1ACE Exercise 6 Investigation 1 6. a. Draw ALL the lines of symmetry on Shape 1 and Shape 2 below. HINT Refer to Problem 1.2 for an explanation of lines of symmetry. Shape 1 Shape 2 b. Do these shapes have rotational symmetry? Shape 1: Shape 2: Explain. HINT Refer back to Problem 1.2 for an explanation of rotational symmetry. 18

2 2ACE Exercises 6 9 Investigation 2 For Exercises 6 9, find the measure of the angle labeled x without measuring. Use the drawings below to help you determine the measurement of angle x in each problem HINT Do not forget to label your answers with the degree sign. 6. x 30 x x x x x x 35 x 19

3 3ACE Exercise 2 Investigation 3 2. Below are sets of regular polygons of different sizes. Use the polygons to complete the table. You may need to measure the length of one side of each polygon and measure one angle of each polygon. Polygon 1 Polygon 2 Polygon 3 Polygon 4 Polygon 5 Polygon 6 Polygon 7 Polygon 8 Polygon 9 Polygon 10 Polygon 11 Polygon 12 Polygon Length of Sides (cm) Sum of Interior Angles Does the length of a side of a regular polygon affect the sum of the interior angle measures? Explain

4 3ACE Exercise 2 (Alternative) Investigation 3 2. Below are sets of regular polygons of different sizes. Remember regular polygons are shapes that have all their sides and all their angles equal. Polygon 1 Polygon 2 Polygon 3 Polygon 4 Polygon 5 Polygon 6 Polygon 7 Polygon 8 Polygon 9 Polygon 10 Polygon 11 Polygon 12 a. What is the sum of the angles for Polygon 1? b. What is the sum of the angles for Polygon 2? c. What is the sum of the angles for Polygon 3? d. Did changing the length of a side of a regular triangle change the sum of the interior angle measures? e. What is the sum of the angles for Polygon 4? f. What is the sum of the angles for Polygon 5? g. What is the sum of the angles for Polygon 6?. Did changing the length of a side of a regular hexagon change the sum of the interior angle measures? 21

5 3ACE Exercise 2 (Alternative, continued) Investigation 3 j.i. What is the sum of the angles for Polygon 7? What is the sum of the angles for Polygon 8? What is the sum of the angles for Polygon 9? l. Did changing the length of a side of a regular rectangle (i.e. a square) change the sum of the interior angle measures? m. What is the sum of the angles for Polygon 10? n. What is the sum of the angles for Polygon 11? o. What is the sum of the angles for Polygon 12? p. Did changing the length of a side of a regular pentagon change the sum of the interior angle measures? q. Does the length of a regular polygon affect the sum of the interior angle measure? r. Explain? 22

6 4ACE Exercise 8 Investigation 4 8. Giraldo and Maria are building a tent. They have two 3-foot poles. In addition, they have a 5-foot pole, a 6-foot pole, and a 7-foot pole. They want to make a triangular shaped doorframe for the tent using both 3-foot poles and one of the other poles. HINT You may want to use polystrips or straw models cut to 3 inches, 3 inches, 5 inches, 6 inches, and 7 inches to test and see which ones will make a triangle with the two 3-foot poles. You can use inches (3, 3, 5, 6, & 7 inches) as a substitute for feet (3, 3, 5, 6 & 7 feet). Which of the longer poles (5 foot, 6 foot, or 7 foot) could be used to form the base of the door? Explain why each pole will or will not work. 5-ft pole: 6-ft pole: 7-ft pole: 23

7 Unit Test 1. For the following polygon: a. Draw in the lines of symmetry. b. Describe the rotational symmetries. 2. a. What is the interior angle sum of a regular pentagon? Explain. b. How many degrees are in one exterior angle of a regular pentagon? HINT This is a regular pentagon. 24

8 Unit Test (continued) 3. A triangle has side lengths measuring 3 and 7. The measurement of the longest side is missing. Ted says that one possibility for the unknown side length is 11. Do you agree with Ted? HINT What do you know about the lengths of sides of a triangle? Explain why or why not. 4. Is it possible for a triangle to have angles with measures 34, 45, and 100? Explain why or why not. 5. Is it possible to make two different quadrilaterals that both have side lengths 7, 7, 9, 9? Explain. HINT You may want to draw a picture. 25

9 Unit Test (continued) 6. In the diagram below, estimate the measures of each numbered angle The diagram below shows rectangle ABCD with diagonal CA. Find the measure of the angle marked x. D C 40 x A B Measure of angle x = 26

10 Unit Test (continued) 8. In the quadrilateral below, the top and bottom sides are parallel. Use the quadrilateral to answer parts (a) (b) a. Find the measures of angles 1, 2, 3, and 4. Explain your reasoning. Measure of angle 1 = Reasoning: Measure of angle 2 = Reasoning: Measure of angle 3 = Reasoning: Measure of angle 4 = Reasoning: b. Find the measure of angles 5 and 6. 27

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