Exam 20: Similarity

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?

Jeff's hot tub is 3 feet deep and holds 1500 gallons of water. He's building a pool that is similar in shape but 9 feet deep. How much water will his pool hold?

Suppose a segment is 8.25 cm long. A) How long is a segment 2times as long as this segment? B) How long is a segment 2 times longer than this segment? . C) How long is a segment 300% longer than this segment?

A) Explain why triangles ACD and AEB in the figure must be similar. B) Knowing that triangles ACD and AEB are similar, find x and y in the figure.

The ruler method was used to enlarge the right triangle in the figure. What is the scale factor? What is x? (Note: This figure is not drawn to scale.)

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

Triangle ABC is similar to triangle DEC, with E corresponding to B. If you know that AC = 6 cm in length, AB = 4 cm, CD = 10 cm, and CE = 13 cm, find the lengths of the other segments and the measures of the angles not given. Be sure to give units. A) Length of BC = _____ B) Measure of angle BCA = _____ C) Measure of angle D = _____ D) Length of DE = _____ E) Measure of angle ECD = _____ F) Measure of angle E = _____

A right rectangular prism with dimensions $\frac { 2 } { 3 }$ by $\frac { 4 } { 3 }$ by $\frac { 8 } { 3 }$ (each in inches) is enlarged by a scale factor of $1 \frac { 1 } { 2 }$ A) The volume of the prism is _____. B) The surface area of the original prism is _____ times as much as the surface area of the larger right rectangular prism.

Triangle A has an area of 50 cm². Triangle B is similar to Triangle A but has sides twice as long. What is the area of Triangle B?

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

Two regular pentagonal pyramids have the following dimensions. Length of base edge Length of lateral edge Pyramid A: 7 centimeters 20 centimeters Pyramid B: 4 centimeters 7 centimeters Are the two pyramids (mathematically) similar? Explain your reasoning.

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.

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

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.)

Explain why the following shapes are similar or are not similar. A) Every two triangles. B) Every two squares.

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

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

Frederick drew a quadrilateral on the chalkboard. He then wanted to draw a new quadrilateral similar to the original one, with a scale factor of 3. This is what he did:When he was done, Frederick was confused because the new quadrilateral did not appear to be "three times as large" as the original. When he was done, Frederick was confused because the new quadrilateral did not appear to be "three times as large" as the original. A) What did Frederick do incorrectly? B) What is the scale factor for the two figures he did draw?

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?

The ruler method was used to shrink the right triangle in the figure. What is the scale factor for the length of the two triangles? What is x? (Note: The figures are not drawn to scale.)