Scaled Relationships

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To investigating Scaled Relationships.

Each of these polygons below is a scaled copy of the others.

  • Study the figures and answer the questions below.​

(1). Each of these polygons is a scaled copy of the others. Name two pairs of corresponding angles. What can you say about the sizes of these angles?

Check your prediction by measuring at least one pair of corresponding angles using a protractor. You can zoom in and out if you need.

(2). Record your measurement of the corresponding angle you chose to the nearest 5°.

The side lengths of the polygons are hard to tell from the grid, but there are other corresponding distances that are easier to compare. Identify the distances in the other two polygons that correspond to DB and AC, and record them in the table below.

(3). Look at the values in the table. What do you notice?

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More Investigation on Scaled Relationships.

Here are two quadrilaterals. Mai says that Polygon ZSCH is a scaled copy of Polygon XJYN, but Noah disagrees.

(1). Do you agree with either of them? Explain your reasoning. Use the app to help you decide.

(2). Record the corresponding distances in the table.

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More Investigation on Scaled Relationships.

Figure 2 is a scaled copy of Figure 1.

(1). Identify the points in Figure 2 that correspond to the points A and C in Figure 1. Label them P and R . What is the distance between P and R?

(2). Identify the points in Figure 1 that correspond to the points Q and S in Figure 2. Label them B and D . What is the distance between B and D?

(3). What is the scale factor that takes Figure 1 to Figure 2?

(4). Figure 2 is a scaled copy of Figure 1. G and H are two points on Figure 1, but they are not shown. The distance between G and H is 1. What is the distance between the corresponding points on Figure 2?

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Here are two quadrilaterals.

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Here is Quadrilateral ABCD.

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