Chapter 7 Quiz -8a
- 1.
Determine if the two figures are similar by using transformations.
- A.
The figures are not similar.
- B.
Similar; a reflection and a dilation map one figure onto the other.
- C.
Similar; a rotation and a dilation map one figure onto the other.
- D.
Similar; a translation and a dilation map one figure onto the other.
Correct Answer
D. Similar; a translation and a dilation map one figure onto the other.Explanation
The correct answer is "Similar; a translation and a dilation map one figure onto the other." This means that the two figures can be transformed into each other through a combination of a translation (moving the figure without changing its size or shape) and a dilation (changing the size of the figure while keeping the same shape).Rate this question:
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- 2.
Determine if the two figures are similar by using transformations.
- A.
The figures are not similar.
- B.
Similar; a rotation and a dilation map one figure onto the other.
- C.
Similar; a translation and a dilation map one figure onto the other.
- D.
Similar; a reflection and a dilation map one figure onto the other.
Correct Answer
A. The figures are not similar.Explanation
The given answer states that the figures are not similar. This means that there is no combination of transformations (rotation, translation, reflection, dilation) that can map one figure onto the other.Rate this question:
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- 3.
A stop sign casts a shadow 8 meters long, while a bush nearby casts a shadow 5.5 meters long. If the stop sign is 4.2 meters high, how tall is the bush?
- A.
10.5 m
- B.
6.1 m
- C.
2.9 m
- D.
1.8 m
Correct Answer
C. 2.9 mExplanation
The height of an object can be determined by using the concept of similar triangles. In this case, we can set up a proportion between the height of the stop sign and the length of its shadow, and the height of the bush and the length of its shadow. The proportion would be: height of stop sign / length of stop sign shadow = height of bush / length of bush shadow. Plugging in the given values, we get: 4.2 m / 8 m = height of bush / 5.5 m. Solving for the height of the bush, we find that it is 2.9 m.Rate this question:
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- 4.
The two triangles shown in the figure are similar. Find the distance d across Kelley’s Pond.
- A.
46 yards
- B.
84 yards
- C.
25 yards
- D.
64 yards
Correct Answer
D. 64 yardsExplanation
The two triangles shown in the figure are similar, which means that their corresponding sides are proportional. By comparing the corresponding sides of the triangles, we can determine that the ratio of the length of the side across Kelley's Pond to the length of the side in the smaller triangle is the same as the ratio of the length of the side across Kelley's Pond to the length of the side in the larger triangle. Since the length of the side in the smaller triangle is 16 yards and the length of the side in the larger triangle is 40 yards, we can set up the proportion: (d/16) = (40/100). Solving for d, we find that d is equal to 64 yards.Rate this question:
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- 5.
Determine whether the triangles are similar. Explain why or why not.
- A.
No; y = 65
- B.
No; x = 85
- C.
Yes; y = 55
- D.
Yes; x = 85
Correct Answer
B. No; x = 85 -
- 6.
A triangle has a side length of 5 centimeters and an area of 15 square centimeters. A similar triangle has a corresponding side length of 25 centimeters. Find the area of the larger triangle.
- A.
375 cm2
- B.
75 cm2
- C.
125 cm2
- D.
625 cm2
Correct Answer
A. 375 cm2Explanation
The area of a triangle is directly proportional to the square of its side length. In this case, the ratio of the side lengths between the two triangles is 25/5 = 5. Therefore, the ratio of their areas is (5^2) = 25. Since the area of the smaller triangle is 15 cm2, the area of the larger triangle can be found by multiplying 15 cm2 by the ratio of their areas, which is 25. Thus, the area of the larger triangle is 15 cm2 * 25 = 375 cm2.Rate this question:
- 7.
Debbie is painting an image on a piece of art canvas. The image she is reproducing is 3 inches by 5 inches. She enlarges the dimensions 4 times. Which of the following statements is NOT true?
- A.
The perimeter of the original image and the perimeter of the new image are related by a scale factor of 4.
- B.
The area of the new image is 4 times the area of the original image.
- C.
The area of the original image and the area of the new image are related by a scale factor of 16.
- D.
The perimeter of the original image is 1 − 4 the perimeter of the new image.
Correct Answer
B. The area of the new image is 4 times the area of the original image.Explanation
When an image is enlarged by a scale factor of 4, the area of the new image is actually 16 times the area of the original image, not 4 times.Rate this question:
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- 8.
Which of the following statements is NOT true if quadrilateral ABCD is congruent to quadrilateral RSTU?
- A.
AB ≅ RS
- B.
CD ≅ TU
- C.
∠T ≅ ∠C
- D.
∠A ≅ ∠U
Correct Answer
D. ∠A ≅ ∠UExplanation
If quadrilateral ABCD is congruent to quadrilateral RSTU, then all corresponding sides and angles of the two quadrilaterals are congruent. Therefore, it is not true that ∠A is congruent to ∠U, as all other corresponding angles are congruent.Rate this question:
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- 9.
Two rectangles are similar. The length and width of the first rectangle is 5 meters by 7 meters. The second rectangle is similar by a scale factor 3. What is the area of the second rectangle?
- A.
216 m2
- B.
105 m2
- C.
315 m2
- D.
189 m2
Correct Answer
C. 315 m2Explanation
The area of a rectangle is calculated by multiplying its length and width. Since the second rectangle is similar to the first one with a scale factor of 3, its length and width will also be scaled up by a factor of 3. Therefore, the length of the second rectangle will be 5 meters * 3 = 15 meters and the width will be 7 meters * 3 = 21 meters. To find the area, we multiply the length and width of the second rectangle: 15 meters * 21 meters = 315 m2.Rate this question:
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- 10.
Which pair of polygons is not similar?
- A.
Option 1
- B.
Option 2
- C.
Option 3
Correct Answer
A. Option 1Explanation
Without knowing the specific polygons mentioned in the options, it is impossible to determine which pair of polygons is not similar. Additional information is needed to provide a proper explanation.Rate this question:
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- 11.
The figures shown are similar. Find the perimeter of the second figure.
- A.
18 cm
- B.
16 cm
- C.
25 cm
- D.
20 cm
Correct Answer
B. 16 cm -
- 12.
Write a proportion comparing the rise to the run for each of the similar slope triangles and find the numeric value.
- A.
1
- B.
-1
- C.
3/4
- D.
-3/4
Correct Answer
A. 1Explanation
The proportion comparing the rise to the run for each of the similar slope triangles is 1. In other words, for every 1 unit of rise, there is 1 unit of run.Rate this question:
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- 13.
Write a proportion comparing the rise to the run for each of the similar slope triangles and find the numeric value.
- A.
1/2
- B.
1/4
- C.
2
- D.
-1/2
Correct Answer
A. 1/2Explanation
The given answer, 1/2, is the correct value for the proportion comparing the rise to the run for each of the similar slope triangles. This means that for every 1 unit increase in the rise, there will be a corresponding increase of 1/2 units in the run.Rate this question:
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- 14.
Determine whether the triangles are similar. If not, explain why not.
- A.
No, b = 110
- B.
No, b = 40
- C.
No, a = 30
- D.
Yes
Correct Answer
D. YesExplanation
The given answer "yes" indicates that the triangles are similar. However, without any additional information or context provided in the question, it is not possible to determine why the triangles are similar. The reason for their similarity could be based on various criteria such as having the same angles or proportional side lengths, but without further details, it is not possible to provide a specific explanation.Rate this question:
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- 15.
Which statement is true concerning any non-vertical line on the coordinate plane?
- A.
All of the slope triangles on the line are congruent
- B.
The slope is the same between any two distinct points on the line.
- C.
In the slope triangles, the ratios of the rise to the run are equal to the absolute value of the y-coordinate.
- D.
The slope varies between any two distinct points on the line.
Correct Answer
B. The slope is the same between any two distinct points on the line.Explanation
The statement "The slope is the same between any two distinct points on the line" is true for any non-vertical line on the coordinate plane. The slope of a line is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. Since the slope is constant for any two distinct points on the line, it means that the line has a constant steepness or inclination throughout its length. This property is a fundamental characteristic of non-vertical lines and is used to define their slope.Rate this question:
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Mar 21, 2023Quiz Edited by
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