Question

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The Odd Man Out!
PART 2:
For each set of figures below, three are similar (meaning that they are related through a sequence of transformations including dilation), and one is an exception. Find the exception in each set of figures and answer the questions for each set. ​

Answer 1

a. exception: C; obtuse angle with a different measure

b. corresponding angles are congruent; corresponding sides are proportional

c. corresponding angles are congruent among the similar triangles; they are not congruent when the triangles are not similar

d. corresponding sides are porportional; they are not proportional when the triangles are not similar

Explanation:

As you know, similar triangles have congruent corresponding angles, and proportional corresponding sides. This gives them the same shape, but they may be of differenent sizes.

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a.

Figure C appears to have a larger smallest angle and a smaller largest angle than the rest of the figures. Its long side relative to its second-longest side appears to be shorter, consistent with a smaller largest angle.

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b.

The similar triangles have congruent corresponding angles and proportional corresponding sides.

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c.

See (b) regarding similar triangles. Non-similar triangles have different angles.

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d.

See (b) regarding similar triangles. Non-similar triangles have different side proportions.