9.6

Warm UpWarm Up

Lesson QuizLesson Quiz

Lesson PresentationLesson Presentation

Identify Symmetry

9.6 Warm-Up

Find the coordinates of the image of A(–3, 8) for each transformation.

1. Reflection in the line y = x

2. Rotation of 90º about the origin

ANSWER (8, –3)

ANSWER (–8, –3)

3. Translation 4 units down

ANSWER (–3, 4)

9.6 Example1

SOLUTION

How many lines of symmetry does the hexagon have?

b. c.

a. Two lines of symmetry.

b. Six lines of symmetry.

c. One line of symmetry.

a.

9.6 Guided Practice

How many lines of symmetry does the object appear to have?

1.

3.

ANSWER 8

ANSWER 5

ANSWER 1

2.

9.6 Guided Practice

4. Draw a hexagon with no lines of symmetry.

SAMPLE ANSWER

9.6 Example 2

Does the figure have rotational symmetry? If so, describe any rotations that map the figure onto itself.

a. Parallelogram

SOLUTION

a. The parallelogram has rotational symmetry. The center is the intersection of the diagonals. A 180° rotation about the center maps the parallelogram onto itself.

9.6 Example 2

Does the figure have rotational symmetry? If so, describe any rotations that map the figure onto itself.

SOLUTION

b. The regular octagon has rotational symmetry.The center is the intersection of the diagonals. Rotations of 45 , 90 , 135 , or 180° about the center all map the octagon onto itself.

o o o

b. Regular octagon

9.6 Example 2

Does the figure have rotational symmetry? If so, describe any rotations that map the figure onto itself.

SOLUTION

c. The trapezoid does not have rotational symmetry because no rotation of 180° or less maps the trapezoid onto itself.

c. Trapezoid

9.6 Guided Practice

Does the figure have rotational symmetry? If so, describe any rotations that map the figure onto itself.

5. Rhombus

6. Octagon

7. Right triangle

ANSWER yes; 180° about the center

yes; 90° or 180° about the center

ANSWER

noANSWER

9.6 Example 3

SOLUTION

The triangle has line symmetry. Three lines of symmetry can be drawn for the figure.

9.6

For a figure with s lines of symmetry, the smallest rotation that maps the figure onto itself has the measure . So, the equilateral triangle has

or 120° rotational symmetry.

Example 3

The correct answer is B.

360° s360° 3

9.6 Guided Practice

8. Describe the lines of symmetry and rotational symmetry of a non-equilateral isosceles triangle.

the altitude, no rotational symmetry

ANSWER

9.6 Lesson Quiz

How many lines of symmetry does each figure have?

1. A Rhombus that is not a square

ANSWER 2

9.6 Lesson Quiz

How many lines of symmetry does each figure have?

2. Equilateral triangle

ANSWER 3

9.6 Lesson Quiz

Does the figure have rotational symmetry? If so, describe the rotations that map the figure onto itself.

3.

ANSWER Yes; 72° , 144°

9.6 Lesson Quiz

Does the figure have rotational symmetry? If so, describe the rotations that map the figure onto itself.

4.

ANSWER no