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Lesson Menu Five-Minute Check (over Lesson 6–5) Main Idea and Vocabulary Example 1:Draw a Reflection Example 2:Reflect a Figure Over an Axis Example 3:Reflect a Figure Over an Axis Example 4:Use a Reflection

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Main Idea/Vocabulary reflection line of reflection transformation image Graph reflections on a coordinate plane.

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Example 1 Draw a Reflection Copy trapezoid STUV below on graph paper. Then draw the image of the figure after a reflection over the given line.

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Example 1 Draw a Reflection Step 1Count the number of units between each vertex and the line of reflection. Step 2Plot a point for each vertex the same distance away from the line on the other side. Step 3Connect the new vertices to form the image of trapezoid STUV, trapezoid S'T'U'V'. Answer:

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1.A 2.B 3.C 4.D Example 1 Copy trapezoid TRAP below on graph paper. Then draw the image of the figure after a reflection over the given line. A.B. C.D.

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Example 2 Reflect a Figure Over an Axis Graph quadrilateral EFGH with vertices E(–4, 4), F(3, 3), G(4, 2) and H(–2, 1). Then graph the image of EFGH after a reflection over the x-axis and write the coordinates of its vertices.

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Example 2 Reflect a Figure Over an Axis The coordinates of the vertices of the image are E'(–4, –4), F'(3, –3), G'(4, –2), and H'(–2, –1).

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Example 2 Reflect a Figure Over an Axis Notice that the y-coordinate of a point reflected over the x-axis is the opposite of the y-coordinate of the original point. same H(–2, 1) opposites E(–4, 4) F(3, 3) G(4, 2) H'(–2, –1) G'(4, –2) F'(3, –3) E'(–4, –4) Answer: E'(–4, –4), F'(3, –3), G'(4, –2), and H'(–2, –1).

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1.A 2.B 3.C 4.D Example 2 Graph quadrilateral QUAD with vertices Q(2, 4), U(4, 1), A(–1, 1), and D(–3, 3). Then graph the image of QUAD after a reflection over the x-axis, and write the coordinates of its vertices. A.Q'(2, –4), U'(4, –1), A'(–1, –1), and D'(–3, –3) B.Q'(–2, –4), U'(–4, –1), A'(1, 1), and D'(3, 3) C.Q'(2, –4), U'(4, –1), A'(1, –1), and D'(3, –3) D.Q'(–2, 4), U'(–4, 1), A'(–1, –1), and D'(–3, –3)

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Example 3 Reflect a Figure Over an Axis Graph quadrilateral ABCD with vertices A(1, 3), B(4, 0), C(3, –4), and D(1, –2). Then graph the image of ABCD after a reflection over the y-axis, and write the coordinates of its vertices.

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Example 3 Reflect a Figure Over an Axis The coordinates of the vertices of the image are A'(–1, 3), B'(–4, 0), C'(–3, –4), and D'(–1, –2).

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Example 3 Reflect a Figure Over an Axis Notice that the x-coordinate of a point reflected over the y-axis is the opposite of the x-coordinate of the original point. opposites D(1, –2) same A(1, 3) B(4, 0) C(3, –4) D'(–1, –2) C'(–3, –4) B'(–4, 0) A'(–1, 3) Answer: A'(–1, 3), B'(–4, 0), C'(–3, –4), and D'(–1, –2).

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1.A 2.B 3.C 4.D Example 3 Graph quadrilateral ABCD with vertices A(2, 2), B(5, 0), C(4, –2), and D(2, –1). Then graph the image of ABCD after a reflection over the y-axis, and write the coordinates of its vertices. A.A'(2, 2), B'(5, 0), C'(4, 2), and D'(2, 1) B.A'(–2, –2), B'(–5, 0), C'(–4, –2), and D'(–2, –1) C.A'(2, –2), B'(5, 0), C'(–4, –2), and D'(2, –1) D.A'(–2, 2), B'(–5, 0), C'(–4, –2), and D'(–2, –1)

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Example 4 ARCHITECTURE Copy and complete the office floor plan shown below so that the completed office has a horizontal line of symmetry. You can reflect the half of the office floor plan shown over the indicated horizontal line. Find the distance from each vertex on the figure to the line of reflection. Then plot a point the same distance away on the opposite side of the line. Connect vertices as appropriate. Answer: Use a Reflection

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Example 4 GAMES Copy and complete the game board shown below so that the completed game board has a vertical line of symmetry. Answer: Interactive Lab: Reflections

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End of the Lesson

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Resources Five-Minute Check (over Lesson 6–5) Image Bank Math Tools Investigating Congruent Triangles Reflections

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1.A 2.B 3.C 4.D Five Minute Check 1 Determine whether the figure has line symmetry. If it does, identify the figure that shows all lines of symmetry. If not, choose none. (over Lesson 6-5) A.B. C.D. none

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1.A 2.B 3.C 4.D Five Minute Check 2 Determine whether the figure has line symmetry. If it does, identify the figure that shows all lines of symmetry. If not, choose none. (over Lesson 6-5) A.B. C.D. none

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1.A 2.B 3.C 4.D Five Minute Check 3 A.yes; 30°, 60°, and 90° B. yes; 45°, 90°, and 180° C. yes; 90°, 180°, and 270° D.no Determine whether the figure has rotational symmetry. If yes, name its angle(s) of rotation. (over Lesson 6-5)

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1.A 2.B 3.C 4.D Five Minute Check 4 A.yes; 45°, 90°, and 180° B. yes; 90°, 180°, and 270° C. yes; 90°, 180°, and 360° D.no Determine whether the figure has rotational symmetry. If yes, name its angle(s) of rotation. (over Lesson 6-5)

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1.A 2.B 3.C 4.D Five Minute Check 5 A.equilateral triangle B.isosceles triangle C.obtuse triangle D.scalene triangle Which polygon has exactly 3 lines of symmetry? (over Lesson 6-5)

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