Learn on PengiBig Ideas Math, Advanced 2Chapter 2: Transformations

Section 2.6: Perimeters and Areas of Similar Figures

In this Grade 7 lesson from Big Ideas Math Advanced 2, students explore how changes in the dimensions of similar figures affect perimeter and area, learning that the ratio of perimeters equals the ratio of corresponding side lengths while the ratio of areas equals the square of that ratio. Students practice finding and applying these ratios using similar rectangles and triangles. The lesson is part of Chapter 2 on Transformations and builds geometric reasoning skills through hands-on activities and coordinate graphing.

Section 1

Similar Figures

Property

Two figures are similar if, and only if:

  1. Their corresponding angles are equal, and
  2. Their corresponding sides are proportional.

Examples

  • A rectangle with sides 4 cm and 6 cm is similar to a rectangle with sides 8 cm and 12 cm. The scale factor is 2.
  • A photograph measuring 4 inches by 6 inches is enlarged to 8 inches by 12 inches. The enlarged photo is similar to the original.

Section 2

Perimeter Ratio of Similar Figures

Property

For similar figures, the ratio of their perimeters equals the ratio of any pair of corresponding side lengths:

Perimeter of Figure 1Perimeter of Figure 2=Side length of Figure 1Corresponding side length of Figure 2\frac{\text{Perimeter of Figure 1}}{\text{Perimeter of Figure 2}} = \frac{\text{Side length of Figure 1}}{\text{Corresponding side length of Figure 2}}

Section 3

Finding Ratios of Corresponding Measurements

Property

For similar figures, the ratio of corresponding measurements is found by dividing one measurement by its corresponding measurement in the other figure: measurement1measurement2\frac{\text{measurement}_1}{\text{measurement}_2}

Examples

Book overview

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Chapter 2: Transformations

  1. Lesson 1

    Section 2.1: Congruent Figures

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  2. Lesson 2

    Section 2.2: Translations

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  3. Lesson 3

    Section 2.3: Reflections

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  4. Lesson 4

    Section 2.4: Rotations

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  5. Lesson 5

    Section 2.5: Similar Figures

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  6. Lesson 6Current

    Section 2.6: Perimeters and Areas of Similar Figures

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  7. Lesson 7

    Section 2.7: Dilations

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Lesson overview

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Section 1

Similar Figures

Property

Two figures are similar if, and only if:

  1. Their corresponding angles are equal, and
  2. Their corresponding sides are proportional.

Examples

  • A rectangle with sides 4 cm and 6 cm is similar to a rectangle with sides 8 cm and 12 cm. The scale factor is 2.
  • A photograph measuring 4 inches by 6 inches is enlarged to 8 inches by 12 inches. The enlarged photo is similar to the original.

Section 2

Perimeter Ratio of Similar Figures

Property

For similar figures, the ratio of their perimeters equals the ratio of any pair of corresponding side lengths:

Perimeter of Figure 1Perimeter of Figure 2=Side length of Figure 1Corresponding side length of Figure 2\frac{\text{Perimeter of Figure 1}}{\text{Perimeter of Figure 2}} = \frac{\text{Side length of Figure 1}}{\text{Corresponding side length of Figure 2}}

Section 3

Finding Ratios of Corresponding Measurements

Property

For similar figures, the ratio of corresponding measurements is found by dividing one measurement by its corresponding measurement in the other figure: measurement1measurement2\frac{\text{measurement}_1}{\text{measurement}_2}

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 2: Transformations

  1. Lesson 1

    Section 2.1: Congruent Figures

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  2. Lesson 2

    Section 2.2: Translations

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  3. Lesson 3

    Section 2.3: Reflections

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  4. Lesson 4

    Section 2.4: Rotations

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  5. Lesson 5

    Section 2.5: Similar Figures

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  6. Lesson 6Current

    Section 2.6: Perimeters and Areas of Similar Figures

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  7. Lesson 7

    Section 2.7: Dilations

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