PRE-ALGEBRA

“Symmetry and Reflections” (9-9)

A figure has symmetry when one half is a mirror image of the other half (in other words, both halves are congruent).

What is “reflectional symmetry”?What is a “line of symmetry”. Example: In the pictures below, the butterfly has one line of symmetry and the

snowflake has six line of symmetry.

What is a “reflection”.

Example: In the figure below, A’B’C’ is a reflection of ABC., because reflected points are the same distance from the line of reflection (A’ and A’ are 4 units from “y”, B and B’ are 3 units from “y”, C and C’ are 2 units from “y”). Note: A’B’C’ ABC.

The line of symmetry divides a figure into two congruent halves. Note: A figure can have more than one line of symmetry.

A reflection is transformation in which a figure is flipped over a line of reflection, so both sides of the line of reflection are mirror images of one another.

4 4

3 3

2 2

PRE-ALGEBRA

Identify the lines of symmetry. Tell how many there are.

a. 

b. 

8 lines of symmetry

Symmetry and ReflectionsLESSON 9-9

Additional Examples

2 lines of symmetry

PRE-ALGEBRA

Reflect the other endpoint, G, which is 4 units away from the x-axis.

Since F is 2 units below the x-axis, F is 2 units above the x-axis.

Draw F G .

FG has endpoints F(–4, –2) and G(–2, –4). Graph FG and the image of FG after a reflection over the x-axis.

Symmetry and ReflectionsLESSON 9-9

Additional Examples

2

2

4

4

PRE-ALGEBRA

Graph y = –1 (in red).

Reflect the other endpoint, G, which is 3 units away from the x-axis.

Since F is 1 unit below the red line, F is 1 unit above the red line.

Draw F G .

FG has endpoints F(–4, –2) and G(–2, –4). Graph FG and the image of FG after a reflection over y = –1.

Symmetry and ReflectionsLESSON 9-9

Additional Examples

11

3

3