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Lesson Plans and Worksheets for Grade 8

Lesson Plans and Worksheets for all Grades

More Lessons for Grade 8

Common Core For Grade 8

### New York State Common Core Math Grade 8, Module 3, Lesson 8

### Lesson 8 Student Outcomes

### Lesson 8 Summary

### NYS Math Module 3 Grade 8 Lesson 8

Example 5

Knowing that a sequence of a dilation followed by a congruence defines similarity also helps determine if two figures are, in fact, similar. For example, would a dilation map triangle onto triangle ? That is, is △ ABC ∼ △ DEF?

Example 6

Again, knowing that a dilation followed by a congruence defines similarity also helps determine if two figures are, in fact, similar. For example, would a dilation map Figure A onto Figure A'? That is, is Figure A ∼ Figure A'

Exercises 1–4

1. Triangle ABC was dilated from center O by scale factor r = 1/2. The dilated triangle is noted by A'B'C'. Another triangle A''B''C'' is congruent to triangle A'B'C' (i.e. △ A'B'C' ≅ △ A''B''C''). Describe the dilation followed by the basic rigid motion that would map triangle A''B''C'' onto triangle ABC.

2. Describe the sequence that would show △ ABC ∼ △ A'B'C'.

3. Are the two triangles shown below similar? If so, describe the sequence that would prove △ ABC ∼ △ A'B'C'. If not, state how you know they are not similar.

4. Are the two triangles shown below similar? If so, describe the sequence that would prove △ ABC ∼ △ A'B'C'. If not, state how you know they are not similar.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Lesson Plans and Worksheets for Grade 8

Lesson Plans and Worksheets for all Grades

More Lessons for Grade 8

Common Core For Grade 8

Examples, videos, and solutions to help Grade 8 students learn why dilation alone is not enough to determine similarity.

Download Worksheets for Grade 8, Module 3, Lesson 8

• Students know the definition of similar and why dilation alone is not enough to determine similarity.

• Given two similar figures, students describe the sequence of a dilation and a congruence that would map one
figure onto the other.

• Similarity is defined as mapping one figure onto another as a sequence of a dilation followed by a congruence (a
sequence of rigid motions).

The notation, △ ABC ∼ △ A'B'C' means that △ ABC is similar to △ A'B'C'.

Classwork

Concept Development

A dilation alone is not enough to state that two figures are similar. Consider the following pair of figures:

Example 1

In the picture below we have a triangle ABC, that has been dilated from center 0, by a scale factor of r = 1/2. It is noted
by A'B'C'. We also have triangle A''B''C'', which is congruent to triangle A'B'C' (i.e. △ A'B'C' ≅ △ A''B''C'').

Example 2

In the picture below, we have a triangle DEF, that has been dilated from center O, by scale factor r = 3. It is
noted by D'E'F'. We also have triangle D''E''F'', which is congruent to triangle D'E'F' (i.e. △ D'E'F' ≅ △ D''E'F'').

Example 3

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

Example 4

In the diagram below, we have two similar figures. Using the notation, we have △ ABC is similar to △ DEF. We want to
describe the sequence of the dilation followed by a congruence that would prove these figures to be similar.

Example 5

Knowing that a sequence of a dilation followed by a congruence defines similarity also helps determine if two figures are, in fact, similar. For example, would a dilation map triangle onto triangle ? That is, is △ ABC ∼ △ DEF?

Example 6

Again, knowing that a dilation followed by a congruence defines similarity also helps determine if two figures are, in fact, similar. For example, would a dilation map Figure A onto Figure A'? That is, is Figure A ∼ Figure A'

Exercises 1–4

1. Triangle ABC was dilated from center O by scale factor r = 1/2. The dilated triangle is noted by A'B'C'. Another triangle A''B''C'' is congruent to triangle A'B'C' (i.e. △ A'B'C' ≅ △ A''B''C''). Describe the dilation followed by the basic rigid motion that would map triangle A''B''C'' onto triangle ABC.

2. Describe the sequence that would show △ ABC ∼ △ A'B'C'.

3. Are the two triangles shown below similar? If so, describe the sequence that would prove △ ABC ∼ △ A'B'C'. If not, state how you know they are not similar.

4. Are the two triangles shown below similar? If so, describe the sequence that would prove △ ABC ∼ △ A'B'C'. If not, state how you know they are not similar.

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