Lesson 06: Similarity | Unit 2: Dilations, Similarity, and Introducing Slope

Draw

For the first diagram, show that the two figures are similar by identifying a sequence of translations, rotations, reflections, and dilations that takes the smaller figure to the larger one. Annotate the image to demonstrate your answer.

Draw

For the second diagram, show that the two figures are similar by identifying a sequence of translations, rotations, reflections, and dilations that takes the smaller figure to the larger one. Annotate the image to demonstrate your answer.

Draw

Measure the side lengths and angles of each polygon. Annotate the image with your measurements.

Multiple Choice

What do you notice about the side lengths and angles of the two polygons after measuring?

• The side lengths are not proportional and the angles are different.
• The side lengths are equal and the angles are proportional.
• The side lengths are proportional and the angles are equal.
• The side lengths are random and the angles are complementary.

Multiple Choice

For the first pair of similar triangles shown in the figure, what is the scale factor to use for a dilation moving the larger triangle to the smaller one?

• 2/1
• 1/2
• 1/3
• 3/2

Multiple Choice

For the second pair of similar triangles shown in the figure, what is the scale factor to use for a dilation moving the larger triangle to the smaller one?

• 0.5
• 1.5
• 2
• 0.25

Multiple Choice

Which sequence of transformations shows that one figure is similar to the other?

• Translation, reflection, and rotation.
• Reflection, rotation, and scaling.
• Dilation, reflection, and shear.
• Dilation, rotation, and translation.

Open Ended

Andre said, “I found two figures that are congruent, so they can’t be similar.” Diego said, “No, they are similar! The scale factor is 1.” Do you agree with either of them? Use the definition of similarity to explain your answer.

Draw

Show that the two figures are similar by identifying a sequence of translations, rotations, reflections, and dilations that takes one figure to the other. Annotate the image to demonstrate the transformations. Context: Figure ABCD and figure EFGH are on a 10 by 10 grid. Letting bottom left corner = (0, 0), A = (1, 9), B = (1, 6), C = (3, 5), D = (2, 6), E = (9, 9), F = (9, 3), G = (5, 1), H = (7, 3).

Multiple Choice

The diagram shows a pair of similar figures, triangle $$ABC$$ and triangle $$ADE$$ . What is the center of dilation that moves the triangle $$ADE$$ to triangle $$ABC$$ ?

• O (1,1)
• O (2,2)
• O (3,3)
• O (0,0)