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Similarity Module 3 Lesson 5

Similarity A’ C’ B’ C B A ~

Similarity Two figures are said to be similar if one can be mapped onto the other using a dilation followed by a congruent transformation (rigid transformations) … or a congruent transformation followed by a dilation.

Example 2 In the diagram below, △ ABC~ △ A'B'C'. Describe the sequence of the dilation followed by a congruence that would prove these figures to be similar.

Example 2 One Possible Solution

Corresponding Sides We can’t use just any two sides to calculate scale factor, we need to look at corresponding sides. Corresponding sides: sides that are in the same relative position B A T L R G 10 m 20 m 8 m 7 m 16 m 14 m

Scale Factor The ratio of corresponding side lengths of a figure and its image after dilation. Scale factor = ? B A T L R G 10 m 20 m 8 m 7 m 16 m 14 m

Example 3 Are the two triangles similar? 6 cm 2 cm 4 cm 3 cm 7.5 cm 5 cm

Example 4 Are the two polygons similar? 8 cm 6 cm 3 cm 15 cm

Example 5 Would a dilation map Figure A onto Figure A'? That is, is Figure A ~ Figure A'?

Example 5 Solution No. Even though two sets of sides are in proportion, there exists no single rigid motion or sequence of rigid motions that would map a four-sided figure to a three- sided figure.

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