Shadows Similar Figures

Solve for x, y, and z using the similar figures.

• x = 16, y = 32, z = 40

• x = 16/3, y = 6, z = 15/2

• x = 3, y = 32/3, z = 40/3

• x = 4/3, y = 8/3, z = 10/3

If a tree casts a 24-foot shadow at the same time that a yardstick casts a 2-foot shadow, find the height of the tree.

• 16 ft

• 144 ft

• 30 ft

• 36 ft

What is the scale factor for mapping △ABC to △DEF?

• 6

• 1/6

• 1/3

• 3

Tell whether the two figures are similar. Explain your reasoning.

• Yes, similar because they are the same shape and side lengths are proportional.

• No, not similar because they are the same shape, but side lengths are not proportional.

• Yes, same shape

• No, different sizes

Are the two figures similar?

• yes

• no

The scale factor of △ABC to △PQR is 2.5. What are the side lengths of △ABC in inches?

• AB = 3, BC = 4, CA = 2

• AB = 2.4, BC = 3.2, CA = 1.6

• AB = 15, BC = 20, CA = 10

• AB = 12, BC = 16, CA = 8

If △ABC ~ △DEF, find the scale factor, k, in the dilation △ABC → △DEF and the measure of b.

• k = 3, b = 3

• k = 1/3, b = 3

• k = 3, b = 1

• k = 1/3, b = 1

△CEF was formed by dilating △CDG. Solve for x.

• x = 5

• x = 6.5

• x = 5.5

• x = 6

Trapezoid ABCD is dilated by a scale factor of 5. What are the coordinates of A'B'C'D'?

• A'(-25, -2), B'(-5, 2), C'(0, -1), D'(-10, -3)

• A'(-25, -10), B'(-5, 10), C'(0, -5), D'(-10, -15)

• A'(1, -2/5), B'(-1/5, 2/5), C'(0, -1/5), D'(-2/5, -3/5)

• A'(-25, -2/5), B'(-5, 2/5), C'(0, -1/5), D'(-10, -3/5)

Find the value of x, given the two similar triangles.

• x = 8

• x = -6

• x = 6

• x = -8