Lesson 12.6 Symmetry pp. 525-527

Objective: To define and illustrate the three types of plane symmetry – line, rotational, and point.

There are three types of plane symmetry. 1. Line 2. Rotational 3. Point

Definition A figure has line symmetry when each half of the figure is the image of the other half under some reflection in a line.

W X V U A B C O

There may be more than one line of symmetry. W X V U O

Definition A figure has rotational symmetry when the image of the figure coincides with the figure after a rotation. The magnitude of the rotation must be less than 360°.

Rotational symmetry of 180° is called point symmetry.

What kind of symmetry does each figure have?

What kind of symmetry does each figure have?

What kind of symmetry does each figure have?

What kind of symmetry does each figure have?

What kind of symmetry does each figure have?

What kind of symmetry does each figure have?

What kind of symmetry does each figure have?

What kind of symmetry does each figure have?

Which figures have rotational symmetry? (1) (2) (3) (4) (5)

Which figures have rotational symmetry? (1) (2) (3)

List the angle of rotation for each rotational symmetry. (1) (2) (3)

Which figures have point symmetry? (1) (2) (3) (4) (5)

Which figures have point symmetry? (1) (2)

Homework pp. 526-527

►A. Exercises How many axes of symmetry does each figure have? 1.

►A. Exercises How many axes of symmetry does each figure have? 2.

►A. Exercises How many axes of symmetry does each figure have? 7.

►B. Exercises 9. Which figures in exercises 1-8 have rotational symmetry?

►B. Exercises 11. Which figures in exercises 1-8 have point symmetry?

►B. Exercises Draw each figure listed in exercises 12- 17 and then draw all lines of symmetry. Identify any figures with rotational symmetry. 15. A concave hexagon

►B. Exercises 19. A figure has 90° rotational symmetry. Will it also have point symmetry?

■ Cumulative Review Let U = the set of integers. A = {x | -3 ≤ x  2 and x is an integer} B = {1, 2, 4, 8, 16, . . . } C = {50, - 9 } D = {x | x is a prime number} 21. Write set C in simpler form; then write the correct subset relation for C.

■ Cumulative Review Let U = the set of integers. A = {x | -3 ≤ x  2 and x is an integer} B = {1, 2, 4, 8, 16, . . . } C = {50, - 9 } D = {x | x is a prime number} 22. Express sets A and D in list form.

■ Cumulative Review Let U = the set of integers. A = {x | -3 ≤ x  2 and x is an integer} B = {1, 2, 4, 8, 16, . . . } C = {50, - 9 } D = {x | x is a prime number} 23. Express set B in set-builder notation.

■ Cumulative Review Let U = the set of integers. A = {x | -3 ≤ x  2 and x is an integer} B = {1, 2, 4, 8, 16, . . . } C = {50, - 9 } D = {x | x is a prime number} 24. Find B  D and A  D.

■ Cumulative Review Let U = the set of integers. A = {x | -3 ≤ x  2 and x is an integer} B = {1, 2, 4, 8, 16, . . . } C = {50, - 9 } D = {x | x is a prime number} 25. Find A  C and B  C.