Math Problem Statement
AC =
Group of answer choices
4
8
16
6
AC = ? Group of answer choices: 4, 8, 16, 6
Solution
The image shows two triangles, and , where is similar to . Given that , and we are solving for , we rely on the properties of similar triangles.
Key Observations:
- (indicated by the equal angles and proportional sides).
- includes both segments and .
- The proportionality of sides holds:
Analysis:
- : This is given.
- and are marked with similar proportions.
- Using similarity, because is double due to the given proportionality.
Answer:
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Related Questions:
- How do you calculate the ratio of two similar triangles?
- What other geometric properties are shared by similar triangles?
- How would you determine the scale factor between two triangles?
- If was halved, how would it affect ?
- Can you apply the Pythagorean theorem to verify side lengths here?
Tip:
Always look for parallel sides and equal angles as clues for similar triangles!
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Math Problem Analysis
Mathematical Concepts
Geometry
Similar Triangles
Proportionality
Formulas
AS/AC = TS/BC (Proportionality of similar triangles)
Theorems
Triangle Similarity Theorem
Suitable Grade Level
Grades 8-10