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.
1
Example 1
How many lines of symmetry?
Solution
2
Example 2
How many lines of symmetry?
Solution
3
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.
Solution
Triangle A is the reflection image of the red
triangle in the blue line through 5 on the xaxis.
Triangle B is the reflection image of the red
triangle in the red line through 3 on the yaxis.
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)
4
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.
5
Example 2
Construct a quadrilateral ABCD on grid paper, where...
A(2,2)
B(4,4)
C(6,4)
D(6,2)
y
7
6
5
B
4
C
3
2
A
D
1
x
0
1
2
3
4
5
6
7
Draw the image of ABCD after performing the following
reflections...
a)
Reflection in the horizontal line through 2 on the y-axis.
y
7
6
5
B
4
C
3
2
A
D
1
x
0
1
2
3
4
5
6
7
Coordinates of the larger shape
A(2,2)
B(4,4)
C(6,4)
C'(6,0)
B'(4,0)
Describe its shape: Pentagon
Describe its symmetry: Line Symmetry
6
b)
Reflection in the vertical line through 6 on the x-axis.
y
y
10
10
9
9
8
8
7
7
6
6
5
5
C
B
4
C
B
4
B'
3
3
2
A
2
D
A
A'
D
1
1
x
x
0
1
2
3
4
5
6
7
8
9
10
0
1
2
3
4
5
6
7
8
9
10
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 trapezoid
Describe its symmetry: line symmetry
7
Reflection in oblique line through (0,0) and (6,6)
c)
y
y
10
10
9
9
8
8
7
7
6
6
5
5
C
B
4
C'
D'
C
B
4
3
3
2
A
1
2
D
A
1
D
x
x
0
1
2
3
4
5
6
7
8
9
10
0
1
2
3
4
5
6
7
8
9
10
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:
Hexagon
Describe its symmetry: line symmetry
The Reflection Line = Line of Symmetry
8
Text Book ­ page 357, #'s 3 ­ 10
Extra Practice 5
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