1. Splash Screen

2. Lesson Menu Five-Minute Check (over Lesson 11–2) Then/Now New Vocabulary Example 1:Rotate a Figure about a Point Example 2:Rotate a Figure about a Point Example 3:Rotations about the Origin Example 4:Real-World Example: Rotational Symmetry

3. Over Lesson 11–2 5-Minute Check 1 A.ΔDEF B.ΔEDF C.ΔEFD D.ΔDFE Which correctly completes the congruence statement ΔACB  Δ___?

4. Over Lesson 11–2 5-Minute Check 2 A.  K B.  M C.  L D.  P Complete the congruence statement if ΔPNO  ΔKML.  N  ___ ?

5. Over Lesson 11–2 5-Minute Check 3 A.NO B.PN C.OP D.ML ___ Complete the congruence statement if ΔPNO  ΔKML. LK  ___ ___ ?

6. Over Lesson 11–2 5-Minute Check 4 A kite is made up of 2 congruent triangles, ΔABC and ΔFGH. Which of the following statements is not true? A.AB  GH B. AC  FH C. AB  FG D. BC  GH ___

7. Then/Now You drew translations and reflections on the coordinate plane. (Lesson 2–7) Define, identify, and draw rotations. Determine if a figure has rotational symmetry.

8. Vocabulary rotation center of rotation rotational symmetry

9. Example 1 Rotate a Figure about a Point Draw the figure shown after a 90° clockwise rotation about point A. Point A stays in the same position. The figure moves one quarter turn clockwise. Answer: '

10. A. B. C. D. Example 1 Which figure is a 270° clockwise rotation of the figure about point S?

11. Example 2 Rotate a Figure about a Point Triangle EFG has vertices E(2, 1), F(1, –1) and G(4, –1). Graph the figure and its image after a clockwise rotation of 90° about vertex F. Then give the coordinates of the vertices for triangle E'F'G'. Step 1 Graph the original figure. Then graph vertex E' after a 90° rotation about vertex F.

12. Example 2 Rotate a Figure about a Point Answer: E'(3, –2), F'(1, –1), and G'(1, –4) Step 2 Graph the remaining vertices after 90° rotations around vertex F. Connect the vertices to form triangle E'F'G'.

13. Example 2 A.90° B.180° C.270° D.360° In the figure, triangle ABC has been rotated about point A to form triangle A'B'C'. How many degrees was it rotated?

14. Example 3 Rotations about the Origin Parallelogram ABCD has vertices A(–3, –1), B(1, –2), C(–1, –4) and D(–5, –3). Graph the parallelogram and its image after a rotation of 180° about the origin. Step 1Graph the original figure on a coordinate plane. Then graph vertex A' after a 180° rotation about the origin.

15. Example 3 Rotations about the Origin Step 2 Graph the remaining vertices after 180° rotations around vertex A. Connect the vertices to form parallelogram A'B'C'D'. Answer: A' (3, 1), B' (–1, 2), C' (1, 4), D' (5, 3)

16. Example 3 A.X'(3, –1), Y'(0, 2), Z'(–4, –3) B.X'(1, –3), Y'(–2, 0), Z'(3, 4) C.X'(–1, 3), Y'(2, 0), Z'(–3, –4) D.X'(–3, –1), Y'(0, –2), Z'(4, –3) Triangle XYZ has vertices X(–3, 1), Y(0, –2), and Z(4, 3). Find the coordinates of the vertices after a rotation of 180° about the origin.

17. Example 4 Rotational Symmetry STAR Determine whether the star shown has rotational symmetry. If it does, describe the angle of rotation. Answer: Yes, the angle of rotation is 72°. So, the angle of rotation is 360° ÷ 5 or 72°. The pattern repeats in 5 even intervals. The star can match itself in five positions.

18. Example 4 A.yes; 45° B.yes; 60° C.yes; 90° D.no DESIGNS Determine whether the design shown has rotational symmetry. If it does, describe the angle of rotation.

19. End of the Lesson