Math Problem Statement
Solve
Solution
To determine which triangles are similar by SSS (Side-Side-Side) similarity, we need to check if the corresponding sides of the triangles are proportional. That is, the ratios of the lengths of corresponding sides should be equal.
Let's analyze the triangles provided:
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Triangle ABC:
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Triangle DEF:
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Triangle GHI:
Comparing the Triangles:
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Comparing Triangle ABC and Triangle DEF:
All three side ratios are equal, so Triangle ABC is similar to Triangle DEF by SSS similarity.
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Comparing Triangle ABC and Triangle GHI:
The side ratios are not all equal, so Triangle ABC is not similar to Triangle GHI.
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Comparing Triangle DEF and Triangle GHI:
The side ratios are not all equal, so Triangle DEF is not similar to Triangle GHI.
Answer:
The correct choice is ABC and DEF.
Do you want details or have any questions about the solution? Here are some related questions to further explore this topic:
- How can you determine the similarity of triangles using the SAS (Side-Angle-Side) criterion?
- If two triangles have one pair of proportional sides and one equal angle, can they be similar?
- What is the difference between similarity and congruence in triangles?
- How do changes in the proportions of side lengths affect the similarity of triangles?
- Can two triangles be similar if their corresponding side lengths are in different ratios?
Tip: When using SSS similarity, always ensure the ratios of corresponding sides are exactly equal; even slight differences indicate the triangles are not similar.
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Math Problem Analysis
Mathematical Concepts
Geometry
Triangle Similarity
Formulas
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Theorems
SSS Similarity Criterion
Suitable Grade Level
Grades 7-9