Unit 3, Lesson 15
Converse of the Pythagorean Theorem
Geometry
Practice
Problem 1
A triangle has sides of length 8, 10, and \(x\). What value of \(x\) makes it the hypotenuse of a right triangle?
Problem 2
Complete each inequality so that it describes possible lengths to make a triangle.
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6, 8, \(x\)
\(\underline{\hspace{.5in}} < x < \underline{\hspace{.5in}}\)
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13, 17, \(y\)
\(\underline{\hspace{.5in}} < y < \underline{\hspace{.5in}}\)
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5, 5, \(z\)
\(\underline{\hspace{.5in}} < z < \underline{\hspace{.5in}}\)
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98, 100, \(a\)
\(\underline{\hspace{.5in}} < a < \underline{\hspace{.5in}}\)
Problem 3
A triangle has sides of length 5, 7, and \(x\).
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Complete the inequality so that it describes possible lengths for \(x\) in an acute triangle.
\(\underline{\hspace{.5in}} < x < \underline{\hspace{.5in}}\)
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Complete the inequality so that it describes possible lengths for \(x\) in an obtuse triangle.
\(\underline{\hspace{.5in}} < x < \underline{\hspace{.5in}}\)