7-1: Dilations
What does the point (1, 2) become after a dilation of 0.5?
(0.5, 1)
What makes a transformation a similarity transformation?
A similarity transformation includes a dilation and possibly one or more rigid motions. A similarity transformation produces a figure that has angles congruent to and sides proportional to the original figure.
How many triangle similarity statements are there? What are they?
3!
(AA~, SSS~, SAS~)
A(2, 7) and A'(6, 21). What is the scale factor?
3
Do similarity transformations produce congruent figures?
No! (Unless the dilation is by a scale factor of 1.)
Draw an example of two similar triangles using SSS~.
Answers will vary. Corresponding sides must be proportional.
True or False: If a figure is dilated by 1/2, it is an enlargement.
False! It is a reduction.
What are the coordinates of A' after A(2, 7) has first been reflected over the x-axis and then dilated by a scale factor of 2?
(4, -14)
If figures are similar, then their corresponding angles are ____________________.
Congruent.
Explain what happens when a figure is dilated by 1.
The pre-image and image are exactly the same.
Write your own example of a similarity transformation.
Answers will vary.
Transformation must include a dilation.
If figures are similar, then their corresponding sides must be_______________________.
Proportional.
PQ and P'Q' are the hypotenuse of a triangle. PQ measures 12 unites and P'Q' measures 9 units. What is the scale factor?
9/12 or 3/4
What are the coordinates of V′ after the transformation (T<3, –2> ◦ D5)(ΔTUV) for T(–1, –1), U(–1, 2), V(2, 1)?
(13, 3)
Triangle ABC ~ Triangle DOG.
Angle A = 20 degrees, Angle B = 50 degrees, and Angle C = 110 degrees.
What is the measure of angle G?
110 Degrees.