1ACE Exercise 17. Name Date Class. 17. Which figure does NOT have rotation symmetry?

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1 1ACE Exercise 17 Investigation Which figure does NOT have rotation symmetry? HINT Rotation symmetry means you can turn the object around its center to a position in which it looks the same as the original position. A. B. C.. 179

2 ACE Exercises Investigation Exercises each give a figure, and its image under a transformation. Tell whether the transformation was a reflection, a rotation, or a translation. Then, indicate the line of reflection, the center and angle of rotation, or the direction and distance of the translation HINT A reflection means that you can draw a line of symmetry that divides the figure into halves that are mirror images. A rotation turns a figure counterclockwise about a point (the center) to a position in which the figure looks the same as the figure in the original position. Is this a reflection, a rotation, or a translation? A translation slides each point of a figure a given distance and direction. If it is a reflection, indicate the reflection line. If it is a rotation, indicate the center and angle of rotation. If it is a translation, indicate the direction and distance of the translation. 11. Is this a reflection, a rotation, or a translation? If it is a reflection, indicate the reflection line. If it is a rotation, indicate the center and angle of rotation. If it is a translation, indicate the direction and distance of the translation

3 ACE Exercises (continued) Investigation 1. Is this a reflection, a rotation, or a translation? If it is a reflection, indicate the reflection line. If it is a rotation, indicate the center and angle of rotation. 1 3 If it is a translation, indicate the direction and distance of the translation Is this a reflection, a rotation, or a translation? If it is a reflection, indicate the reflection line. If it is a rotation, indicate the center and angle of rotation. If it is a translation, indicate the direction and distance of the translation

4 3ACE Exercises 1 4 Investigation 3 In Exercises 1 4, there are four pairs of congruent figures. In each pair, match each side and angle of the first shape with its congruent partner in the second shape. HINT The first one has been done as an example. 1. A B K L C N M a. Matching sides: AB LK A LM BC KN C MN b. Matching angles: A = L B = K C = N = M. C P Q E a. Matching sides: b. Matching angles: R 18

5 3ACE Exercises 1 4 (continued) Investigation 3 3. H J X Y Z I a. Matching sides: b. Matching angles: 4. B A E a. Matching sides: b. Matching angles: C T P S Q R 183

6 4ACE Exercise 9 Investigation 4 9. In the diagram below, cables extend in opposite directions from the top of a tower to the ground. Use what you know about congruent triangles to determine whether the two cables are the same length. Q R cable cable P U T S a. How can you tell if two triangles (triangle PQU and triangle SRT) are congruent? b. Are there any angles and sides of triangle PQU that are congruent to triangle SRT? c. Are triangles PQU and SRT congruent? Explain how you know. d. Is line PQ the same length as line SR? Explain how you know. 184

7 4ACE Exercise 1 1. Pentagon PQRST has rotational symmetry about point C with a 7 angle of rotation. Investigation 4 P T Q C S R HINT Remember, rotational symmetry means that you can turn the object around its center to a position in which it looks the same as the original position. What does this symmetry tell you about the measures of: a. angles in the pentagon? b. side lengths of the pentagon? c. segments from C to each of the vertices of the pentagon? 185

8 5ACE Exercise 16 Investigation What single transformation is equivalent to a 90 (counterclockwise) rotation about the origin followed by a 70 (counterclockwise) rotation about the origin? HINT A 90 counterclockwise rotation is a rotation that moves an object 90 from its origin to the left (i.e., counterclockwise moves images to the left on a graph and clockwise moves things to the right). y 4 90 o counterclockwise 4 O 4 x The new image of the point (, ) following a 90 rotation is (, ) O 4 70 o counterclockwise y 4 x A 70 counterclockwise rotation is a rotation that moves an object 70 degrees to the left. A 70 counterclockwise rotation is three 90 counterclockwise rotations. (, ) following a 90 counterclockwise rotation is (, ) (, ) following a 90 counterclockwise rotation is (, ) (, ) following a 90 counterclockwise rotation is (, ) What single transformation is equivalent to a 90 (counterclockwise) rotation about the origin followed by a 70 (counterclockwise) rotation about the origin? 186

9 Unit Test 1. For the regular pentagon shown at the right: a. escribe any reflection symmetries. Be sure to sketch all lines of reflection. HINT Remember, reflection symmetries divide the figures into halves so that each half is a mirror image of the other (they are the same). b. escribe any rotation symmetries. What is the center of rotation? What is the angle of rotation? HINT Rotational symmetries are those that allow a figure to be rotated less than a full turn around a point and still look the same as the original. Are there any other angles that will rotate the figure to a look-alike position? What are they?. a. Under a particular transformation, A is the image of A and B is the image of B. Give a detailed description of the transformation. A B A B C b. Use a ruler and an angle ruler or protractor to help you draw the image of trapezoid ABC above under the transformation you described in part (a). 187

10 Unit Test (continued) 3. The large triangle below is made from congruent triangles. J 1 E A B C H a. If you moved Triangle 1 so it fit exactly on Triangle, which vertices would be matched? F I G b. Carefully describe a combination of transformations that would move Triangle 1 so that it exactly matches Triangle. You may add lines or points to the diagram if you need to. 4. a. Jake drew the triangle below in the Match Game. Which measurements of angles and sides can he give his partner to ensure that she draws a congruent triangle? A B C b. What two measurements can he give his partner to ensure that she draws a similar triangle? 188

11 Unit Test (continued) 5. The segment EF is a line of reflection symmetry for trapezoid ABC; the measure of C is 55 ; the measure of CB = 3.6; the measure of AE = and the measure of C = 8. Find the measures of EB, F, FC, A, and angles A, B, and. EB A E B F FC A 3.6 A B F 55 C 8 Explain your reasoning. 6. Use the graph below to answer parts (a) and (b). 4 y A 4 B A C O 4 4 x a. If Figure ABC is translated so that the image of A is A at ( 3, 1), then what will the coordinates of the image of be after the translation (i.e., )? HINT is the result of the same translation as A. rawing the translation of Figure ABC to A B C may help. b. escribe a rule that translates any point of Figure ABC so that the image of A is A. 189