Geometry
Similarity and Dilations
Day 2 HW
Name:__________________________________
1. Examine the two triangles below. They are drawn to scale.
a. Are the triangles similar? Justify your answer.
b. Write a mathematical statement saying that the two triangles are similar.
2. Use what you know about similar figures to answer the following questions:
a) Assume one triangle has side lengths 6, 7, and 10 units while another has side lengths 3, 4, and 5 units.
Are these triangles similar? How do you know?
b) The pentagons at right are similar. What are the values
of x and y?
c) Give a possible sequence of transformations that would take the pentagon on the left to the figure on
the right.
3.
Casey is back at it! Now she wants you to enlarge the block “U” for her spirit flag.
a) Copy the U onto graph paper
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b) Dilate the U with a scale factor of 2 from point D. What is
the height of the new U?
c) Find the ratio of the perimeters. What do you notice?
d) Casey dilated the U so that it has a height of 10. What
was her scale factor? What is the base of this new U?
Use you determine the perimeter without adding up
all of the sides? Justify.
4. After seeing Casey enlarge the “U” in problem 2-22, Al has
an idea. He drew a 60° angle, as shown in Diagram #1 at
right. Then, he extended the sides of the angle so that they
are twice as long, as shown in Diagram #2. “Therefore, the
new angle must have measure 120°,” he explained. Do you
agree? Discuss this with your team and write a response to
Al.
5. Rochida drew ΔABC at right and then dilated through the point A
to create ΔAB′C′.
a. Why are the two triangles similar? Write a similarity statement.
b. Rochida decides to redraw the shape as two separate triangles,
as shown at right. Write and solve a proportion to find x using
the corresponding sides.
c. Write a different proportion and solve. Did you
determine the same value for x
6. Al noticed that the ratio of the perimeters of two similar polygons is equal to the ratio of the side
lengths. “What about the area? Does it grow the same way?” he wondered.
a. Find the perimeter and area of the triangle above.
b. Test Al’s question by enlarging the triangle by a scale factor
of 3. Then find the new perimeter and area.
c. Answer Al’s question: Does the perimeter increase by a scale factor of 3? Does the area increase by a scale
factor of 3? Explain what happened