Exploring Similar Polygons in Geometry

Lesson 7.3 covers similar polygons, explaining that they have the same shape but different sizes. The concept of scale factor is introduced, showing how it relates to the proportionality of side lengths in similar polygons. Examples with triangles and quadrilaterals illustrate how to calculate scale factors and solve for unknown side lengths. The lesson concludes with a discussion on the ratio of perimeters in similar polygons, reinforcing the relationship between scale factor and perimeter ratios.

What does it mean for two polygons to be similar?

• They have the same size but different shapes.

• They have the same shape but different sizes.

• They have the same angles but different side lengths.

• They have different shapes and sizes.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Which symbol is used to denote similarity between two polygons?

• ≈

• ≅

• ∼

• ≠

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

What is a scale factor?

• The sum of the side lengths of two similar polygons.

• The proportion of the side lengths of two similar polygons.

• The difference in side lengths of two similar polygons.

• The ratio of the angles of two similar polygons.

Tags

CCSS.7.G.A.1

If a right triangle with sides 3, 4, and 5 is scaled by a factor of 2, what are the new side lengths?

• 1.5, 2, 2.5

• 9, 12, 15

• 3, 4, 5

• 6, 8, 10

Tags

CCSS.7.G.A.1

In similar quadrilaterals, which of the following is true about their corresponding angles?

• They are supplementary.

• They are congruent.

• They are proportional.

• They are complementary.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Given a scale factor of 2:3, if one side of a smaller quadrilateral is 20, what is the corresponding side length in the larger quadrilateral?

• 30

• 15

• 40

• 10

Tags

CCSS.7.G.A.1

If the scale factor from a smaller to a larger quadrilateral is 2:3, what is the length of a side in the smaller quadrilateral if the corresponding side in the larger quadrilateral is 21?

• 14

• 7

• 10.5

• 28

Tags

CCSS.7.G.A.1

Using a scale factor of 2:3, if a side in the larger quadrilateral is 12, what is the corresponding side length in the smaller quadrilateral?

• 4

• 6

• 18

• 8

Tags

CCSS.7.G.A.1

What is the length of a side in the larger quadrilateral if the corresponding side in the smaller quadrilateral is 10 and the scale factor is 2:3?

• 15

• 30

• 20

• 5

Tags

CCSS.7.G.A.1

What is the ratio of the perimeters of two similar quadrilaterals if the scale factor of their sides is 2:3?

• 3:2

• 1:1

• 2:3

• 4:9