Transformation Geometry - Answers

Explain why triangles ACD and AEB are similar. Triangles ACD and AEB are similar because the measures of two angles of ACD are the same as those of two angles of AEB. b. Knowing that triangles ACD and AEB are similar, find x in the picture below. Scale factor = 7.2 / 4 = 9 / 6 = 1.8 x = 1.8 * 4 = 7.2 cm 2. Identify the type of transformation which moves: Fig. 1 to Fig. A: Glide Reflection Fig. 1 to Fig. C: Translation Fig. 1 to Fig. B: Rotation Fig. 1 to Fig. D: Reflection 4. Sketch the images of the figure under the isometries described at right. Read directions. Translate the figure A by vector label that A. Then reflect A through line label that A. Then rotate A "90" about P. Label the final result A'. 5. Add to the figure so the result will have: a. Line symmetry, but no rotational symmetry. b. Rotational symmetry, but no line symmetry. 6. Draw all lines of symmetry for each of the following figures. How many has each? a. None b. 6 (3 of each type shown) c. 5 (all the same from vertex to midpoint of opposite side) 7. What is the smallest angle of rotational symmetry for the figures shown? a. 60° b. 360° 8. A regular decagon has 10 lines of symmetry and 10 rotational symmetries, with the smallest angle of rotational symmetry being 36 degrees. 5. Use the center and an appropriate dilation of the plane to create a figure A'B'C' similar to ABC, with each dimension of A'B'C' 3 times as large as the original. Use a ruler! Label! Each segment, for instance OB, is extended to a new length three times as long. So the length of OB' is 3 times the length of OB. Thus the scale of any triangle (for instance OAB) is multiplied by 3: OA'B' has sides 3 times the length of the sides of OAB. 6. Depending on the type of isometry, find vector of translation, or the line of reflection, or the center and angle of rotation that takes figure 1 to figure 2. Show your work!   a. Line reflection b. Rotation Angle of rotation: -90 degrees (close to it) Center of rotation: (0, 0) (found using the bisectors of AA', BB', where A' and B' are the images after rotation) 7. Use compass and straightedge to construct the altitude through A. AE is the altitude from A. The method shown is the most commonly used.