Lesson 14
Side Length Quotients in Similar Triangles
Problem 1
These two triangles are similar. What are \(a\) and \(b\)? Note: the two figures are not drawn to scale.
Solution
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Problem 2
Here is triangle \(ABC\). Triangle \(XYZ\) is similar to \(ABC\) with scale factor \(\frac 1 4\).
- Draw what triangle \(XYZ\) might look like.
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How do the angle measures of triangle \(XYZ\) compare to triangle \(ABC\)? Explain how you know.
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What are the side lengths of triangle \(XYZ\)?
- For triangle \(XYZ\), calculate (long side) \(\div\) (medium side), and compare to triangle \(ABC\).
Solution
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Problem 3
The two triangles shown are similar. Find the value of \(\frac d c\).
Solution
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Problem 4
The diagram shows two nested triangles that share a vertex. Find a center and a scale factor for a dilation that would move the larger triangle to the smaller triangle.
Solution
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(From Unit 2, Lesson 10.)Problem 5
Which is a scaled copy of Polygon A? Identify a pair of corresponding sides and a pair of corresponding angles. Compare the areas of the scaled copies.
Solution
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(From Unit 2, Lesson 2.)Problem 6
A map of Colorado says that the scale is 1 inch to 20 miles or 1 to 1,267,200. Are these two ways of reporting the scale the same? Explain your reasoning.
Solution
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(From Unit 2, Lesson 7.)