Use the following information to answer the question.
Triangle ABC has side lengths AB=16, BC=13, and AC=7.
Triangle DEF has side lengths DE=4, EF=3.25, and DF=1.75.
Janna needs to prove △ABC∼△DEF.
Which methods can she use to help her prove the triangles are similar by the SSS Similarity Theorem?
Select all that apply.
A. ACDF=EFBC=DFAC=4
B. ABDE=BCEF=4
C. DEAB=EFBC=ACDF=14
D. DEAB=EFBC=DFAC=14
E. ACDF=BCEF=ABDE=4
A and B?
Where's the answer?
where's Ms. Sue?
Hmm, looking at the options, I have to say there seems to be a bit of confusion. The SSS Similarity Theorem states that if the ratios of the corresponding sides of two triangles are equal, then the triangles are similar.
Let's analyze the options:
A. ACDF=EFBC=DFAC=4 - This is not relevant to the SSS Similarity Theorem, as it does not compare corresponding side lengths.
B. ABDE=BCEF=4 - Similarly, this option does not compare corresponding side lengths.
C. DEAB=EFBC=ACDF=14 - Oops, this doesn't match up either. The side lengths in the corresponding positions are not equal.
D. DEAB=EFBC=DFAC=14 - Nope, this one doesn't work either. The side lengths don't match up as necessary.
E. ACDF=BCEF=ABDE=4 - This one doesn't comply either, as the side lengths are not in the correct corresponding positions.
It looks like none of the options mentioned are suitable for proving the similarity of the triangles using the SSS Similarity Theorem. I guess Janna will have to look for another approach. Keep trying, Janna!
To prove that two triangles are similar using the SSS (Side-Side-Side) similarity theorem, Janna needs to show that the ratios of the corresponding sides are equal.
Let's analyze the given answer choices one by one:
A. ACDF = EFBC = DFAC = 4
This answer choice does not provide the ratios of the corresponding sides. It only states the side lengths without any ratio relationship. Therefore, it cannot be used to prove triangle similarity.
B. ABDE = BCEF = 4
Similar to option A, this answer choice only states the side lengths without any ratio. Thus, it cannot be used to prove triangle similarity.
C. DEAB = EFBC = ACDF = 14
This answer choice provides ratios of corresponding sides. The ratio DE/EF = 4/3.25, EF/BC = 3.25/13, and AC/DF = 7/1.75. However, these ratios are not equal, so this option does not satisfy the SSS similarity theorem.
D. DEAB = EFBC = DFAC = 14
This option provides ratios of corresponding sides. The ratio DE/EF = 4/3.25, EF/BC = 3.25/13, and DF/AC = 1.75/7. These ratios are equal, satisfying the SSS similarity theorem. Therefore, this option can be used to prove triangle similarity.
E. ACDF = BCEF = ABDE = 4
Similar to options A and B, this answer choice only states the side lengths without any ratio relationship. Thus, it cannot be used to prove triangle similarity.
Therefore, the correct answer is D. Janna can use the ratios DE/EF = 4/3.25, EF/BC = 3.25/13, and DF/AC = 1.75/7 to help prove the similarity of triangles ABC and DEF by the SSS similarity theorem.
well, let me see
16/4 = 4
7/1.75 = 4
13/3.25 = 4 remarkable, so similar
as for your choices, I do not know what you mean.