Math Problem Statement
Find GP in the given triangle with the given segment lengths.
Solution
The problem involves finding the length of segment in a triangle with parallel segments. We are given the lengths of , , and . Since is parallel to , triangles and are similar by AA similarity.
To find , we can set up a proportion using the corresponding sides of the similar triangles:
Substituting the known values:
Simplify the right side:
Now, solve for :
The closest option is 2.1, so that would be the correct choice.
Would you like further details or have any questions?
Related Questions:
- What property allows triangles to be similar when they have parallel sides?
- How can we verify that the ratio between the corresponding sides is correct?
- What would happen if the triangles were not similar? Could we still solve the problem?
- How do you simplify a fraction like ?
- Why is it important to round to the nearest option in this case?
Tip:
Always check if two triangles share a common angle and if their corresponding sides are proportional to confirm similarity.
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Math Problem Analysis
Mathematical Concepts
Similar triangles
Proportions
Geometry
Formulas
GP / FG = PQ / GH
GP = FG * (PQ / GH)
Theorems
AA Similarity Theorem
Suitable Grade Level
Grades 8-10