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© Boardworks 20141 of 10
Congruence and Similarity
© Boardworks 20142 of 10
Information
© Boardworks 20143 of 10
Objects with exactly the same shape and size are congruent.
Are triangles ABC and PQR congruent?
AB = PQ, BC = QR,
and AC = PR.
A = P, B = Q,
and C = R.
Congruent shapes
If two shapes are congruent, their corresponding lengths and angles are the same.
© Boardworks 20144 of 10
Transformations review
© Boardworks 20145 of 10
Exploring transformations
© Boardworks 20146 of 10
If an image is produced by dilation of a pre-image, the two shapes are not congruent. Instead, we say they are similar.
Similar shapes have the same angle sizes but different side lengths.
The corresponding side lengths of two similar shapes are always in the same ratio.
A = P, B = Q,
and C = R.
AB:PQ = BC:QR = AC:PR
Similar shapes
Are triangles ABC and PQR similar?
© Boardworks 20147 of 10
What happens when a figure is reflected in parallel mirror lines placed at equal distances?
Parallel mirror lines
Are the resulting images congruent or similar?
© Boardworks 20148 of 10
Reflecting a figure in two parallel mirror lines is equivalent to a single translation.
M1 M2
Suppose we have two parallel mirror lines M1 and M2.
We can reflect shape A in mirror line M1 to produce the image A’.
We can then reflect shape A’ in mirror line M2 to produce the image A’’.
How can we map A onto A’’ in a single transformation?
Combining transformations
A A’ A’’
© Boardworks 20149 of 10
M2
M1
A A’
A’’
We can reflect shape A in mirror line M1 to produce the image A’.
We can then reflect shape A’ in mirror line M2 to produce the image A’’.
How can we map A onto A’’ in a single transformation?
Reflection in two perpendicular lines is equivalent to a single rotation of 180°.
Suppose we have two perpendicular mirror lines M1 and M2.
Perpendicular mirror lines
© Boardworks 201410 of 10
Transformation shape sorter