Scaled Relationships

Warmup

Activity #1

investigate 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 above, is a scaled copy of the others.

(a.) Name two pairs of corresponding angles.

(b.) 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 in the applet below. You can zoom in and out using the scroll wheel of your mouse if you need. You can get additional help is you check the box “Extend Sides”.

(2.) In the table below, 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?

Activity #2

More Investigation on Scaled Relationships.

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

• Examine the two polygons and answer the questions that follow.

(1.) Who do you agree with? Explain your reasoning. Use the applet to help you decide.

• Record the corresponding distances in the table.

Activity #3

More Investigation on Scaled Relationships.

Figure 2 is a scaled copy of Figure 1.

• Examine the two figures in the applet below as you pay attention to the corresponding sides and angles.

• Identify the points in Figure 2 that correspond to the points A and C in Figure 1.

• Label them as P and R .

(1.) What is the distance between P and R?

• Identify the points in Figure 1 that correspond to the points Q and S in Figure 2.

• Label them B and D .

(2.) 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?

Challenge #1

Here are two quadrilaterals.

Challenge #2

Here is Quadrilateral ABCD.

Challenge #3

Quiz Time