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More Lessons for Geometry

Common Core For Geometry

Worksheets for Geometry, Module 2, Lesson 14

Student Outcomes

- Students understand that similarity is reflexive, symmetric, and transitive.
- Students recognize that if two triangles are similar, there is a correspondence such that corresponding pairs of angles have the same measure and corresponding sides are proportional. Conversely, they know that if there is a correspondence satisfying these conditions, then there is a similarity transformation taking one triangle to the other respecting the correspondence.

**Similarity**

Classwork

**Example 1**

We said that for a figure π΄ in the plane, it must be true that π΄~π΄. Describe why this must be true.

**Example 2**

We said that for figures π΄ and π΅ in the plane so that π΄~π΅, then it must be true that π΅~π΄. Describe why this must be true.

**Example 3**

Based on the definition of similar, how would you show that any two circles are similar?

**Example 4**

Suppose β³ π΄π΅πΆ β β³ π·πΈπΉ and that, under this correspondence, corresponding angles are equal and corresponding sides are proportional. Does this guarantee that β³ π΄π΅πΆ and β³ π·πΈπΉ are similar?

**Example 5**

a. In the diagram below, β³ π΄π΅πΆ~ β³ π΄β²π΅β²πΆβ². Describe a similarity transformation that maps
β³ π΄π΅πΆ to β³ π΄β²π΅β²πΆβ².

b. Joel says the sequence must require a dilation and three rigid motions, but Sharon is sure there is a similarity
transformation composed of just a dilation and two rigid motions. Who is right?

**Lesson Summary**

- Similarity is reflexive because a figure is similar to itself.
- Similarity is symmetric because once a similarity transformation is determined to take a figure to another, there are inverse transformations that can take the figure back to the original.

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