~ 1.4 ~

Scaled Relationships

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Learning Targets

I can use corresponding distances and corresponding angles to tell whether one figure is a scaled copy of another.
When I see a figure and its scaled copy, I can explain what is true about corresponding angles.
When I see a figure and its scaled copy, I can explain what is true about corresponding distances.

Notes

When a figure is a scaled copy of another figure, we know that:

All distances in the copy can be found by multiplying the corresponding distances in the original figure by the same scale factor, whether or not the endpoints are connected by a segment. For example, Polygon STUVWX is a scaled copy of Polygon ABCDEF. The scale factor is 3. The distance from T to X is 6, which is three times the distance from Bto F.
All angles in the copy have the same measure as the corresponding angles in the original figure, as in these triangles.

These observations can help explain why one figure is not a scaled copy of another.

For example, even though their corresponding angles have the same measure, the second rectangle is not a scaled copy of the first rectangle, because different pairs of corresponding lengths have different scale factors, 2⋅(½) = 1 but 3⋅(2/3) = 2.

Activities

4.1 Three Quadrilaterals (Part 1)

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. Record your measurements to the nearest 5∘.

4.2 Three Quadrilaterals (Part 2)

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

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

4.3 Scaled or Not Scaled?

Here are two quadrilaterals.

Mai says that Polygon ZSCH is a scaled copy of Polygon XJYN, but Noah disagrees. Do you agree with either of them? Explain or show your reasoning.
Study the table below with the corresponding distances in the table. What do you notice?
Study the table below of corresponding angles. What do you notice?
Do these results change your answer to the first question? Explain.

Here are two more quadrilaterals.

5. Kiran says that Polygon EFGH is a scaled copy of ABCD, but Lin disagrees. Do you agree with either of them? Explain or show your reasoning.

Lesson Summary

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