Math Problem Statement
Solution
To find the value of in the given diagram, where lines , , and are parallel and cut by two transversal lines, we can use the property of similar triangles.
Step-by-Step Explanation:
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Identify Corresponding Angles and Ratios:
- Since the lines , , and are parallel, the triangles formed by the transversals are similar.
- Therefore, the corresponding sides of the similar triangles are proportional.
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Set Up the Proportion: The corresponding sides in the two triangles are proportional, so we can set up the following proportion using the given values:
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Solve for : Simplifying: So, .
Final Answer:
The value of is approximately 15.6.
Would you like more details or clarifications on the steps? Here are some related questions:
- How can we confirm that the triangles are similar?
- Why do the parallel lines allow us to set up a proportion between the triangles?
- How can we verify the accuracy of the result?
- What happens if the transversals were not parallel?
- Can we use angle relationships to approach this problem differently?
Tip: When working with similar triangles, always check for corresponding angles and sides to set up accurate proportions.
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Math Problem Analysis
Mathematical Concepts
Geometry
Similar Triangles
Proportions
Formulas
Corresponding side ratios in similar triangles
Theorems
Triangle Proportionality Theorem
Suitable Grade Level
Grades 8-10