Question 1

Given the following picture, expand it using a scale factor of 2 and the given center.

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Question 2

The two shapes below are similar. Find the missing angle size, y, and the missing length, x. Justify your answers.

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Question 3

The triangles are deliberately not drawn to correct scale.  
A) How do you know that the two triangles are similar?
B) Find x and y. (Show your work for credit.)

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The answer of The triangles are deliberately not drawn to...

Question 4

In a photograph of two buildings, building P is 5 centimeters tall and building Q is 7 centimeters tall. In an enlargement of the photograph, building P is 8 centimeters tall. How tall is building Q in the enlargement?

Accepted Answer

The height of the buildings in the photograph and the enlargement are proportional. The height of building P increased from 5 cm to 8 cm, which is a factor of $\frac{8}{5}$. Applying the same factor to building Q's original height (7 cm), the height in the enlargement is $7 \times \frac{8}{5} = 11\frac{1}{5}$ cm.

Question 5

What is the length of x, to the nearest tenth centimeter?

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Question 6

What is the length of y, to the nearest tenth centimeter?

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Question 7

Refer to the similar figures below. What is the length of x, to the nearest tenth centimeter?

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Question 8

Two pentagons have the following lengths of sides.
Pentagon A: 7 centimeters, 7 centimeters, 7 centimeters, 7 centimeters, 10 centimeters
Pentagon B: 4 centimeters, 4 centimeters, 4 centimeters, 4 centimeters, 7 centimeters
Are Pentagons A and B similar? Explain your decision.

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The answer of Two pentagons have the following lengths of...

Question 9

Triangle A and triangle B are similar. The area of triangle A is 560 square centimeters. The area of triangle B is 35 square centimeters. How long would a segment in triangle A be if the corresponding segment in triangle B is 4 centimeters?

Accepted Answer

The ratio of the areas of similar triangles is equal to the square of the ratio of their corresponding sides. Therefore, if the area of triangle A is 560 square centimeters and the area of triangle B is 35 square centimeters, the ratio of their areas is 560/35 = 16. This means the ratio of the lengths of their corresponding sides is the square root of 16, which is 4. If a segment in triangle B is 4 centimeters, the corresponding segment in triangle A would be 4 times longer, making it 4 * 4 = 16 centimeters.

Question 10

Susan is 166 centimeters tall, and in the afternoon she casts a shadow about 55 centimeters long. Her sister, who is standing next to her, casts a shadow about 35 centimeters long. About how tall is Susan's sister (to the nearest centimeter)?

Accepted Answer

Using the concept of similar triangles, the ratio of Susan's height to her shadow length is the same as her sister's height to her shadow length. Therefore, (166/55) = (x/35), solving for x gives approximately 106 centimeters.

Question 11

A triangle is similar to a larger triangle that has lengths three times as long as the corresponding lengths in the smaller triangle. How large is the angle in the smaller triangle that corresponds to a 30° angle in the larger triangle?

Accepted Answer

In similar triangles, corresponding angles are equal. Therefore, the angle in the smaller triangle that corresponds to a 30° angle in the larger triangle is also 30°.

Question 12

What would you have to do to determine whether another quadrilateral EFGH (not shown) is similar to ABCD in the figure?

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Question 13

Treat the measurements in the drawing below as accurate, even though the drawings are intentionally "off." Are the two quadrilaterals similar? Explain.

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Question 14

You want to make a larger, similar version of the trapezoid below so that the 4-centimeter side will be 10 centimeters in the larger version.
A) How long will the other three sides of the larger trapezoid be?
B) What are the sizes of the angles in the larger version?

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Question 15

If the two polyhedra below are similar and oriented alike, then what are the values of x and y rounded to the nearest tenth?

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Question 16

Two regular pentagonal pyramids have the following dimensions.
 
  $\begin{array} { l l l } 
& \text { Length of base edge } & \text { Length of lateral edge } \
\text { Pyramid A: } & 7 \text { centimeters } & 20 \text { centimeters } \
\text { Pyramid B: } & 4 \text { centimeters } & 7 \text { centimeters }
\end{array}$ 
Are the two pyramids (mathematically) similar? Explain your reasoning.

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Question 17

A right rectangular prism has a volume of 2 cubic inches. A second right rectangular prism is similar to the first one and has a volume of 128 cubic inches.
A) What is the scale factor to go from the first prism to the second?
B) What is the scale factor to go from the second prism to the first?

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Question 18

If a cube has edges that are 2 centimeters long, what is the total surface area of a larger similar cube with a scale factor of 2.3?

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Question 19

Suppose you have an L-shaped figure such as the one below. What is the volume of a figure similar to this one rounded to the nearest tenth, with a scale factor of 2.8? Each cube has a volume of 1 cubic unit.

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Question 20

Each face of the small cubes making the shape below has an area of 1 square unit.
A) 
Surface area: _____
Volume: _____
  
B) Suppose another prism is similar to the one above but two times larger in all dimensions. What is the surface area and volume of the new prism? Write enough to make your thinking clear

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The answer of Each face of the small cubes making...

Quiz 20: Similarity

Given the following picture, expand it using a scale factor of 2 and the given center.

The two shapes below are similar. Find the missing angle size, y, and the missing length, x. Justify your answers.

The triangles are deliberately not drawn to correct scale. A) How do you know that the two triangles are similar? B) Find x and y. (Show your work for credit.)

In a photograph of two buildings, building P is 5 centimeters tall and building Q is 7 centimeters tall. In an enlargement of the photograph, building P is 8 centimeters tall. How tall is building Q in the enlargement?

What is the length of x, to the nearest tenth centimeter?

What is the length of y, to the nearest tenth centimeter?

Refer to the similar figures below. What is the length of x, to the nearest tenth centimeter?

Two pentagons have the following lengths of sides. Pentagon A: 7 centimeters, 7 centimeters, 7 centimeters, 7 centimeters, 10 centimeters Pentagon B: 4 centimeters, 4 centimeters, 4 centimeters, 4 centimeters, 7 centimeters Are Pentagons A and B similar? Explain your decision.

Triangle A and triangle B are similar. The area of triangle A is 560 square centimeters. The area of triangle B is 35 square centimeters. How long would a segment in triangle A be if the corresponding segment in triangle B is 4 centimeters?

Susan is 166 centimeters tall, and in the afternoon she casts a shadow about 55 centimeters long. Her sister, who is standing next to her, casts a shadow about 35 centimeters long. About how tall is Susan's sister (to the nearest centimeter) ?

A triangle is similar to a larger triangle that has lengths three times as long as the corresponding lengths in the smaller triangle. How large is the angle in the smaller triangle that corresponds to a 30° angle in the larger triangle?

What would you have to do to determine whether another quadrilateral EFGH (not shown) is similar to ABCD in the figure?

Treat the measurements in the drawing below as accurate, even though the drawings are intentionally "off." Are the two quadrilaterals similar? Explain.

You want to make a larger, similar version of the trapezoid below so that the 4-centimeter side will be 10 centimeters in the larger version. A) How long will the other three sides of the larger trapezoid be? B) What are the sizes of the angles in the larger version?

If the two polyhedra below are similar and oriented alike, then what are the values of x and y rounded to the nearest tenth?

A right rectangular prism has a volume of 2 cubic inches. A second right rectangular prism is similar to the first one and has a volume of 128 cubic inches. A) What is the scale factor to go from the first prism to the second? B) What is the scale factor to go from the second prism to the first?

If a cube has edges that are 2 centimeters long, what is the total surface area of a larger similar cube with a scale factor of 2.3?

Suppose you have an L-shaped figure such as the one below. What is the volume of a figure similar to this one rounded to the nearest tenth, with a scale factor of 2.8? Each cube has a volume of 1 cubic unit.

Each face of the small cubes making the shape below has an area of 1 square unit. A) Surface area: _ Volume: _ B) Suppose another prism is similar to the one above but two times larger in all dimensions. What is the surface area and volume of the new prism? Write enough to make your thinking clear