1.
Selena is painting an image on a piece of art canvas. The image she is reproducing is 4 inches by 6 inches. She enlarges the dimensions 3 times. Which of the following statements is NOT true?
Correct Answer
C. The area of the new image is 3 times the size of the original image.
Explanation
When Selena enlarges the dimensions of the original image by 3 times, the area of the new image will actually be 9 times the size of the original image. Therefore, the statement "The area of the new image is 3 times the size of the original image" is not true.
2.
Bill is 72 inches tall and casts a 60 inch shadow. His son, who is standing next to him, casts a 50 inch shadow. How tall is his son?
Correct Answer
A. 60 in.
Explanation
Since Bill is 72 inches tall and his shadow is 60 inches long, we can use the concept of similar triangles to find the height of his son. The ratio of Bill's height to his shadow length is 72/60, which simplifies to 6/5. Since the son's shadow length is 50 inches, we can set up the proportion 6/5 = x/50, where x represents the son's height. Solving for x, we find that the son's height is 60 inches.
3.
Which of the following statements is not true if triangle JKL is congruent to triangle RST?
Correct Answer
C. ∠K ≅ ∠T
Explanation
If triangle JKL is congruent to triangle RST, it means that the corresponding sides and angles of the triangles are equal. Therefore, if angle K is congruent to angle T, it is true and not false.
4.
Write a proportion comparing the rise to the run for each of the similar slope triangles and find the numeric value.
Correct Answer
B. 1/2
Explanation
The proportion comparing the rise to the run for each of the similar slope triangles is 1/2. This means that for every 1 unit of rise, there is a corresponding 2 units of run.
5.
Determine whether the triangles are similar. If not, explain why not.
Correct Answer
B. Yes
6.
The two triangles shown in the figure are similar. Find the distance d across the river.
Correct Answer
D. 25 m.
Explanation
The two triangles shown in the figure are similar, which means that their corresponding sides are proportional. In this case, we can set up a proportion using the given information. Let's denote the length of the shorter side of the smaller triangle as x, and the length of the corresponding side of the larger triangle as y. We can then set up the proportion: x/16 = y/81. Solving for y, we find y = 81x/16. Since we are looking for the distance across the river, which is the longer side of the larger triangle, we need to find y when x = 18 (the length of the shorter side of the smaller triangle). Plugging in the values, we find y = 81(18)/16 = 81(9)/8 = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81(9/8) = 81
7.
Write a proportion comparing the rise to the run for each of the similar slope triangles and find the numeric value.
Correct Answer
D. -2
Explanation
The given answer, -2, is the numeric value obtained by comparing the rise to the run for each of the similar slope triangles. In a slope triangle, the rise represents the vertical change and the run represents the horizontal change. By comparing the rise to the run in each triangle, we can determine the ratio of vertical change to horizontal change. In this case, the rise is -2 and the run is 1, resulting in a ratio of -2/1, which simplifies to -2.
8.
The figures shown are similar. Find the perimeter of the second figure.
Correct Answer
A. 25.2 mm
Explanation
The perimeter of a figure is the total length of all its sides. Since the figures shown are similar, it means that they have the same shape but possibly different sizes. Therefore, the perimeter of the second figure can be found by multiplying the scale factor between the two figures by the perimeter of the first figure. Without any additional information, we cannot determine the scale factor or the perimeter of the first figure. Hence, it is not possible to provide an explanation for the given correct answer.
9.
A lakefront building that is 40 feet high casts a shadow on the water. How long is that shadow if a 18-foot high truck parked nearby casts an 9-foot shadow?
Correct Answer
D. 20 ft.
Explanation
The height of the truck is proportional to the length of its shadow. If the 18-foot high truck casts a 9-foot shadow, then a 40-foot high building would cast a shadow that is double the length. Therefore, the shadow of the lakefront building would be 20 feet long.
10.
Find the value of x in the similar polygons below.
Correct Answer
B. 6 ft.
Explanation
The value of x can be found by setting up a proportion between the corresponding sides of the similar polygons. In this case, we can set up the proportion 15/6 = x/3. Cross multiplying, we get 15*3 = 6*x, which simplifies to 45 = 6x. Dividing both sides by 6, we find that x = 45/6 = 7.5. However, since the options provided do not include 7.5, the closest value is 6 ft. Hence, the correct answer is 6 ft.
11.
Triangle ABC ~ DEF. Each side of Δ ABC is 3/2 times longer than the corresponding sides of Δ DEF. If the perimeter of Δ ABC is 36 centimeters, what is the perimeter of Δ DEF?
Correct Answer
C. 24 cm
Explanation
Since each side of triangle ABC is 3/2 times longer than the corresponding sides of triangle DEF, it means that the ratio of the sides of ABC to DEF is 3/2. Therefore, if the perimeter of ABC is 36 cm, the perimeter of DEF would be 2/3 times smaller, which is 24 cm.
12.
Which pair of polygons is not similar?
Correct Answer
C. Option 3
Explanation
Without knowing the specific polygons mentioned in the options, it is not possible to provide a specific explanation as to why Option 3 is not similar to the other polygons. The reason could vary depending on the specific shapes and their corresponding properties.
13.
Determine if the two figures are similar by using transformations.
Correct Answer
A. Similar; a reflection and a dilation map one figure onto the other.
Explanation
The correct answer is that the figures are similar because a reflection and a dilation can be used to map one figure onto the other. This means that the two figures have the same shape, but possibly different sizes and orientations.
14.
Determine if the two figures are similar by using transformations.
Correct Answer
C. The figures are not similar.
Explanation
The given answer is stating that the figures are not similar. This means that there is no combination of transformations such as reflection, rotation, translation, or dilation that can map one figure onto the other.
15.
Two rectangles are similar. The length and width of the first rectangle is 3 meters by 5 meters. The second rectangle is similar by a scale factor 4. What is the area of the second rectangle?
Correct Answer
B. 240 m^{2}
Explanation
The area of a rectangle is calculated by multiplying its length by its width. Since the second rectangle is similar to the first one by a scale factor of 4, all its dimensions are multiplied by 4. Therefore, the length of the second rectangle is 3 * 4 = 12 meters and the width is 5 * 4 = 20 meters. Multiplying these dimensions together gives us the area of the second rectangle, which is 12 * 20 = 240 m2.