Starters Find the geometric mean between 8 and

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

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

Find cos A for ΔABC if m C = 90, AB = x, AC = y, and CB = z. A. B. C. D.

Find sin A for ΔABC if m C = 90, AB = x, AC = y, and CB = z. A. B. C. D.

Find tan B for ΔABC if m C = 90, AB = x, AC = y, and CB = z. A. B. C. D.

If m A = 42, AB = 7, and BC = 6 in ΔABC, what is m B? A. 26. 5 B. 35. 0 C. 51. 3 D. 86. 7

9. 1 Reflections You identified reflections and verified them as congruence transformations. • Draw reflections in the coordinate plane.

• line of reflection

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

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 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 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 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:

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.

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) 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) B(3, 2) C(4, – 1) D(2, – 3) → → A'(1, – 1) B'(3, – 2) C'(4, 1) D'(2, 3)

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

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) B(3, 2) C(4, – 1) D(2, – 3) → → A'(– 1, 1) B'(– 3, 2) C'(– 4, – 1) D'(– 2, – 3)

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

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)

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) 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) B(3, 2) C(4, – 1) D(2, – 3) → → A'(1, 1) B'(2, 3) C'(– 1, 4) D'(– 3, 2)

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

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)