To find an unknown length in two similar triangles, you would need to know the lengths of corresponding sides of the triangles and the length of at least one side from one of the triangles.
Steps to find the unknown length:
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Identify Corresponding Sides: Similar triangles have corresponding sides that are proportional. First, identify the sides that correspond between the two triangles.
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Use Proportions: Set up a proportion based on the corresponding sides of the triangles. If triangle A has a side \( a \) and triangle B has a corresponding side \( b \), then the proportion can be written as: \[ \frac{a}{b} = \frac{x}{y} \] where \( x \) is the unknown length you want to find, and \( y \) is the length of the corresponding side in the triangle you have.
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Cross-Multiply: Once the proportion is set up, cross-multiply to solve for the unknown length \( x \): \[ a \cdot y = b \cdot x \]
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Solve for the Unknown: Rearrange the equation to isolate \( x \): \[ x = \frac{a \cdot y}{b} \]
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Calculate: Substitute the known values into the equation to calculate the unknown length \( x \).
By following these steps, you can find an unknown side length in similar triangles using proportional relationships.