1. Section 16.1: Dilations

2. Objective:
By following instructions, students will be able to:
Explain how a dilation transforms a figure.

3. The center of dilation is the fixed point about which all other points are transformed by a dilation. The ratio of the lengths of corresponding sides in the image and the preimage is called the scale factor. Dilations preserve angle measures.

4. explain 1A
Determine if the transformation on the coordinate plane is a dilation. If it is, give the scale factor.
Preserves angle measure:
Preserves orientation:
Ratio of corresponding sides:
Is this transformation a dilation?

5. explain 1B
Determine if the transformation on the coordinate plane is a dilation. If it is, give the scale factor.
Preserves angle measure:
Preserves orientation:
Ratio of corresponding sides:
Is this transformation a dilation?

6. Your-Turn #1
Determine if the transformations are dilations.

7. Find the measure of each angle and complete the statements below.
explain 2A
Find the length of each segment.
OA = OB = OC =
OA′ = OB′ = OC′ =
Next, find the ratio of the sides.
Similary, find the length of each side of the triangle.
Next, find the ratio of the sides of the triangle.
Compare the ratios of the sides and the ratios of the sides of the triangle. What special pattern do you notice about them?

8. explain 2B
Find the center of dilation, the measure of each angle, and complete the statements below.
Find the length of each segment.
OA = OB = OC =
OA′ = OB′ = OC′ =
Next, find the ratio of the sides.
Similary, find the length of each side of the triangle.
Next, find the ratio of the sides of the triangle.
Compare the ratios of the sides and the ratios of the sides of the triangle. What special pattern do you notice about them?

9. Your-Turn #2

10. Revisit Objective:
Did we…
Explain how a dilation transforms a figure?

11. HW:
Sec 16.1 page 632 #s 2-15