1. State the new coordinates after performing the dilation (3x, 3y).
Bell Ringer (5 min.)
State the new coordinates after performing the dilation (3x, 3y). 5

2. UNIT 2 • SIMILARITY, CONGRUENCE, AND PROOF
Pre-Assessment
UNIT 2 • SIMILARITY, CONGRUENCE, AND PROOF

3. Does the graph below represent a dilation?
a. Yes, because the preimage sides are parallel with the corresponding image sides.
b. No, because the preimage sides are not parallel with the corresponding image sides.
c. Yes, because there is a single scale factor and a center of dilation.
d. No, because the scale factors of the image sides are not all consistent with the preimage sides. 1

4. 2. Determine the scale factor of the dilation below.
a. 𝒌=𝟐 b. 𝒌= 𝟏 𝟐
c. 𝒌= 𝟏 𝟒 d. 𝒌=𝟏 1

5. 3. Determine the scale factor of the dilation below.
a. k = 1.07
b. k = 2.5
c. k = 0.4
d. k = 9.2 1

6. 4. 𝑨𝑩 is 6. 7 units long. If 𝑨𝑩 is dilated. by a scale factor of k = 3
4. 𝑨𝑩 is 6.7 units long. If 𝑨𝑩 is dilated by a scale factor of k = 3.2, what is the length of 𝑨′𝑩′ ?
a units
b. 2.1 units
c. 0.5 unit
d. 1 unit 1

7. 5. ∆FGH has vertices F (3, –5), G (8, –6), and H (6, –7)
5. ∆FGH has vertices F (3, –5), G (8, –6), and H (6, –7). If ∆ FGH is dilated through the origin with a scale factor of 3 4 , what are the vertices of ∆ F′G′H′? 1

8. Properties of Dilations E. Q
Properties of Dilations E.Q. How are the pre-image and image similar in dilations? How are they different? 2 1

9. Properties of Dilations
Shape, orientation, and angles are preserved.
All sides change by a single scale factor, k.
Corresponding sides in the preimage and image are parallel.
The corresponding points of the figure are collinear with the center of dilation. 3

10. center of dilation - a point through which a dilation takes place
Definitions
center of dilation - a point through which a dilation takes place
corresponding sides - sides of two figures that lie in the same position relative to the figure
enlargement - a dilation of a figure where the scale factor is greater than 1
reduction - a dilation where the scale factor is between 0 and 1 3

11. 𝑘= length of image side length of preimage side
scale factor - the ratio of any two corresponding lengths in two similar geometric figures
𝑘= length of image side length of preimage side 3

12. Page 9: Is the following transformation a dilation?

13. P. 10, Example 2: Is the following transformation a dilation
P.10, Example 2: Is the following transformation a dilation? Justify your answer using the properties of dilations.

14. P. 10, Example 3: The following transformation represents a dilation
P.10, Example 3: The following transformation represents a dilation. What is the scale factor? Does this indicate enlargement, reduction, or congruence?