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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 Lesson Menu

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

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

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

A kite is made up of 2 congruent triangles, ΔABC and ΔFGH 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 ___ 5-Minute Check 4

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

rotation center of rotation rotational symmetry Vocabulary

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

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

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. Example 2

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

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

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 1 Graph the original figure on a coordinate plane. Then graph vertex A' after a 180° rotation about the origin. 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) Example 3

Triangle XYZ has vertices X(–3, 1), Y(0, –2), and 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. 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) Example 3

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

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

End of the Lesson