Embed Size (px)
Citation preview
1
Section 7.5 - Reflections and Line Symmetry
Page 353 textbook
Line Symmetry - a shape has line symmetry when a line divides the shape into two congruent parts, so that one is the image of the other.
2
Example 1
How many lines of symmetry?
Solution
3
Example 2
How many lines of symmetry?
Solution
4
Solution
Example 3
Identify the triangles that are related to the red triangle by a line of reflection. Describe the position of each line of symmetry.
Triangle A is the reflection image of the red triangle in the blue line through 5 on the x-axis.
Triangle B is the reflection image of the red triangle in the red line through 3 on the y-axis.
Triangle C is not a reflection image of the red triangle.
Triangle D is the reflection image of the red triangle in the green line through points (9,1) and (1,9)
5
Reflections
We can use a coordinate grid to draw shapes and their reflection images.
How can we complete a shape given its line of Symmetry??
Example 1
Solution
The red line is the line of reflection. each image point is the same distance from this line as the corresponding original point.
6
Example 2
Construct a quadrilateral ABCD on grid paper, where...
A(2,2)B(4,4)C(6,4)D(6,2)
0 1 2 3 4 5 6 7
1
2
3
4
5
6
7
x
y
A
B C
D
Draw the image of ABCD after performing the following reflections...
a) Reflection in the horizontal line through 2 on the y-axis.
0 1 2 3 4 5 6 7
1
2
3
4
5
6
7
x
y
A
B C
D
Coordinates of the larger shapeA(2,2)B(4,4)C(6,4)C'(6,0)B'(4,0)
Describe its shape: PentagonDescribe its symmetry: Line Symmetry
7
b) Reflection in the vertical line through 6 on the x-axis.
0 1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
7
8
9
10
x
y
B C
DA
0 1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
7
8
9
10
x
y
B C
DA
B'
A'
Write the coordinates of the larger shape ABB'A'
A(2,2)B(4,4)B'(8,4)A'(10,2)
Describe the new shape: isosceles trapezoidDescribe its symmetry: line symmetry
8
c) Reflection in oblique line through (0,0) and (6,6)
0 1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
7
8
9
10
x
y
A
B C
D
0 1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
7
8
9
10
x
y
A
B C
D
D' C'
Write the coordinates of the larger shape AD'C'BCD
A(2,2)D'(2,6)C'(4,6)B(4,4)C(6,4)D(6,2)
Describe its shape: HexagonDescribe its symmetry: line symmetry
The Reflection Line = Line of Symmetry
9
Text Book page 357, #'s 3 10Extra Practice 5
10
11
12
13
14
15
16
