1.
Problem 2. Are the two figures similar? If so what is the similarity statement. Check 2 of the following choices.
Correct Answer(s)
A. Similar
C. Triangle CBA is similar to Triangle FGH
Explanation
The given answer is correct because the statement "Triangle CBA is similar to Triangle FGH" indicates that the two triangles have the same shape but possibly different sizes. Similarity in geometry means that the corresponding angles of the two figures are equal and the corresponding sides are proportional. Therefore, if Triangle CBA is similar to Triangle FGH, it means that the angles of the two triangles are equal and the sides are proportional, confirming that the figures are similar.
2.
Problem 4. The triangles are similar, complete the similarity statement.
Triangle JKL is similar to Triangle _______.
Correct Answer
A. Triangle TUV
Explanation
The similarity statement for the given triangles is Triangle JKL is similar to Triangle TUV. This is because the order of the vertices in the similarity statement must match the order of the corresponding vertices in the triangles. In this case, J corresponds to T, K corresponds to U, and L corresponds to V. Therefore, the correct similarity statement is Triangle JKL is similar to Triangle TUV.
3.
Porblem 6. True or False. Are the triangles similar?
Correct Answer
B. False
Explanation
The question asks whether the triangles are similar. Similar triangles have the same shape but may have different sizes. To determine if two triangles are similar, we need to compare their corresponding angles and side lengths. However, the question does not provide any information about the triangles or their properties. Therefore, we cannot determine if the triangles are similar or not based on the given information.
4.
Problem 7. The two triangle are similar. Complete the similarity statement.
Triangle TUV is similar to Triangle ______.
Correct Answer
B. QRS
Explanation
The similarity statement for two triangles states that their corresponding angles are congruent and their corresponding sides are proportional. In this case, the given triangles TUV and QRS are similar because they have corresponding angles that are congruent. Therefore, the correct similarity statement is "Triangle TUV is similar to Triangle QRS."
5.
Problem 10. Is Triangle FGH similar to Triangle VUW?
Correct Answer
B. False
Explanation
In order for two triangles to be similar, their corresponding angles must be congruent and their corresponding sides must be proportional. Without any additional information or given measurements, it is not possible to determine if Triangle FGH is similar to Triangle VUW. Therefore, the correct answer is False.
6.
Problem 11. What is the length of FS and FR?
Correct Answer
A. FS=32 and FR=52
Explanation
The given answer states that FS has a length of 32 and FR has a length of 52. This means that FS is shorter than FR.
7.
Problem 13. In triangle LJK, LJ=28, KJ=x. In triangle RPQ, RP=42, PQ=33. The two triangles are similar. What is the value of x?
Correct Answer
B. 22
Explanation
Since the two triangles are similar, their corresponding sides are proportional. In triangle LJK, LJ=28 and KJ=x. In triangle RPQ, RP=42 and PQ=33. We can set up a proportion to find the value of x:
LJ/KJ = RP/PQ
28/x = 42/33
Cross multiplying, we have:
33 * 28 = 42 * x
924 = 42x
Dividing both sides by 42, we find:
x = 924/42 = 22
Therefore, the value of x is 22.
8.
Problem 14. TriangleTUV is similar to Triangle MLK. UV = 60, KL = 130 and LM = 117. What is the length of UT?
Correct Answer
C. 54
Explanation
Since Triangle TUV is similar to Triangle MLK, we can use the property of similar triangles that states corresponding sides are proportional. Therefore, we can set up the following proportion:
UT/ML = UV/KL
Substituting the given values, we have:
UT/117 = 60/130
Cross-multiplying and solving for UT, we get:
UT = (117 * 60) / 130 = 54
9.
Problem 16. Triangle VPW is similar to Triangle QPR. PV = 9, PQ = 18, and PR = 22, what is the length of PW?
Correct Answer
A. 11
Explanation
Since triangle VPW is similar to triangle QPR, we can set up a proportion using the corresponding sides. The length of PV is 9 and the length of PQ is 18. The length of PW is unknown, and the length of PR is 22. Setting up the proportion, we have PW/PR = VP/PQ. Plugging in the given values, we get PW/22 = 9/18. Simplifying the proportion, we have PW/22 = 1/2. Cross multiplying, we get PW = 22/2 = 11. Therefore, the length of PW is 11.
10.
Problem 18. Triangle ABC is similar to Triangle FED. AB = 77, BC = 11x + 11, FE = 21 and DE = 30, what is the value of x?
Correct Answer
B. 9
Explanation
Since Triangle ABC is similar to Triangle FED, the corresponding sides are proportional. We can set up the proportion AB/FE = BC/DE. Plugging in the given values, we get 77/21 = (11x + 11)/30. Cross multiplying and solving for x, we find that x = 9.
11.
Problem 19. Triangle JUT is similar to Triangle JKL. JU = (-4+4x), JK = 64, JT=27 and JL = 72. What is the value of x?
Correct Answer
A. 7
Explanation
Triangle JUT is similar to triangle JKL, which means that their corresponding angles are equal and their corresponding sides are proportional. In this case, we are given that JU = -4 + 4x and JK = 64. We also know that JT = 27 and JL = 72.
To find the value of x, we can set up a proportion using the corresponding sides of the triangles:
(JU / JK) = (JT / JL)
((-4 + 4x) / 64) = (27 / 72)
Cross multiplying and simplifying the equation, we get:
72(-4 + 4x) = 64(27)
-288 + 288x = 1728
288x = 2016
x = 7
Therefore, the value of x is 7.