Starter(s) Find the geometric mean between 8 and 15. State the exact answer. A. B. C. D. 5-Minute Check 1

Determine whether the numbers 6, 9, and 12 are the measures of the sides of a right triangle. A. yes B. no 5-Minute Check 2

Find cos A for ΔABC if mC = 90, AB = x, AC = y, and CB = z. 5-Minute Check 3

Find sin A for ΔABC if mC = 90, AB = x, AC = y, and CB = z. 5-Minute Check 4

Find tan B for ΔABC if mC = 90, AB = x, AC = y, and CB = z. 5-Minute Check 5

If mA = 42, AB = 7, and BC = 6 in ΔABC, what is mB? 5-Minute Check 6

Draw reflections in the coordinate plane. You identified reflections and verified them as congruence transformations. Draw reflections. Draw reflections in the coordinate plane. Then/Now

line of reflection Vocabulary

Draw the reflected image of quadrilateral ABCD in line n. 1) Draw the reflected image of quadrilateral ABCD in line n. A. B. C. D. Example 1

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Example 2) Reflect a Figure in a Horizontal or Vertical Line A. Quadrilateral JKLM has vertices J(2, 3), K(3, 2), L(2, –1), and M(0, 1). Graph JKLM and its image over x = 1. Example 3

Example 2) Reflect a Figure in a Horizontal or Vertical Line Use the horizontal grid lines to find a corresponding point for each vertex so that each vertex and its image are equidistant from the line x = 1. Answer: Example 3

Example 2) Reflect a Figure in a Horizontal or Vertical Line B. Quadrilateral JKLM has vertices J(2, 3), K(3, 2), L(2, –1), and M(0, 1). Graph JKLM and its image over y = –2. Example 3

Example 2) Reflect a Figure in a Horizontal or Vertical Line Use the vertical grid lines to find a corresponding point for each vertex so that each vertex and its image are equidistant from the line y = –2. Answer: Example 3

2) A. Quadrilateral ABCD has vertices A(1, 2), B(0, 1), C(1, –2), and D(3, 0). Graph ABCD and its image over x = 2. A. B. C. D. Example 3

2) B. Quadrilateral WXYZ has vertices W(2, 4), X(3, 3), Y(2, 0), and Z(0, 2). Graph WXYZ and its image over y = –1. A. B. C. D. Example 3

Multiply the y-coordinate of each vertex by –1. (x, y) → (x, –y) Example 3) Reflect a Figure in the x- or y-axis A. Graph quadrilateral ABCD with vertices A(1, 1), B(3, 2), C(4, –1), and D(2, –3) and its image reflected in the x-axis. Multiply the y-coordinate of each vertex by –1. (x, y) → (x, –y) A(1, 1) → A'(1, –1) B(3, 2) → B'(3, –2) C(4, –1) → C'(4, 1) D(2, –3) → D'(2, 3) Example 4

Example 3) Reflect a Figure in the x- or y-axis Answer: Example 4

Multiply the x-coordinate of each vertex by –1. (x, y) → (–x, y) Example 3) Reflect a Figure in the x- or y-axis B. Graph quadrilateral ABCD with vertices A(1, 1), B(3, 2), C(4, –1), and D(2, –3) and its reflected image in the y-axis. Multiply the x-coordinate of each vertex by –1. (x, y) → (–x, y) A(1, 1) → A'(–1, 1) B(3, 2) → B'(–3, 2) C(4, –1) → C'(–4, –1) D(2, –3) → D'(–2, –3) Example 4

Example 3) Reflect a Figure in the x- or y-axis Answer: Example 4

3) A. Graph quadrilateral LMNO with vertices L(3, 1), M(5, 2), N(6, –1), and O(4, –3) and its reflected image in the x-axis. Select the correct coordinates for the new quadrilateral L'M'N'O'. A. L'(3, –1), M'(5, –2), N'(6, 1), O'(4, 3) B. L'(–3, 1), M'(–5, 2), N'(–6, –1), O'(–4, –3) C. L'(–3, –1), M'(–5, –2), N'(–6, 1), O'(–4, 3) D. L'(1, 3), M'(2, 5), N'(–1, 6), O'(–3, 4) Example 4

3) B. Graph quadrilateral LMNO with vertices L(–1, 0), M(1, 1), N(2, –2), and O(0, –4) and its reflected image under the y-axis. Select the correct coordinates for the point M' in the new quadrilateral L'M'N'O'. A. L'(–1, 0), M'(1, –1), N'(2, 2), O'(0, 4) B. L'(1, 0), M'(–1, 1), N'(–2, –2), O'(0, –4) C. L'(1, 0), M'(–1, –1), N'(–2, 2), O'(0, 4) D. L'(0, –1), M'(1, 1), N'(–2, 2), O'(–4, 0) Example 4

Interchange the x- and y-coordinates of each vertex. (x, y) → (y, x) Example 4) Reflect a Figure in the Line y = x Quadrilateral ABCD with vertices A(1, 1), B(3, 2), C(4, –1), and D(2, –3). Graph ABCD and its image under reflection of the line y = x. Interchange the x- and y-coordinates of each vertex. (x, y) → (y, x) A(1, 1) → A'(1, 1) B(3, 2) → B'(2, 3) C(4, –1) → C'(–1, 4) D(2, –3) → D'(–3, 2) Example 5

Example 4) Reflect a Figure in the Line y = x Answer: Example 5

4) Quadrilateral EFGH has vertices E(–3, 1), F(–1, 3), G(1, 2), and H(–3, –1). Graph EFGH and its image under reflection of the line y = x. Select the correct coordinates for the point H' in the new quadrilateral E'F'G'H'. A. E'(–3, –1), F'(–1, –3), G'(1, –2), H'(–3, 1) B. E'(3, –1), F'(1, –3), G'(–1, 2), H'(3, –1) C. E'(1, –3), F'(3, –1), G'(2, 1), H'(–1, –3) D. E'(–1, 3), F'(–3, 1), G'(–2, –1), H'(1, 3) Example 5

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