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Use the converse of the Pythagorean theorem.Use the converse of the Pythagorean theorem.
Determine whether a triangle is a
triangle.
Apply the converse of the
real-world scenarios.
theorem to
Words to Know
Write the letter of the definition next to the matching word as you work through the lesson. You may use the glossary to help you.
substitute
deduce
Pythagorean theorem
converse
right triangle
A. to infer; to draw a conclusion
B. to take the place of; to replace
C. a triangle having an interior angle measuring 90 degrees
D. the theorem stating that the sum of the squares of the lengths of the legs in a right triangle is equal to the square of the length of the hypotenuse
E. statement formed by switching the hypothesis and the conclusion of a conditional
Does a triangle with side lengths 10, 70 , and 30 form a right triangle?
a2 + b2 = c2
70 10
2 22+
=
70 + 30 = 100
= 100
8 70
30 6
< <
< <
Since these three side lengths satisfy the Pythagorean theorem, I know that they
do form a triangle.
Interpret a Real-World Scenario
REAL-WORLD CONNECTION
A window frame appears to be rectangular. The sides of the window frame are 82 inches and 60 inches, while the length of the diagonal is 102 inches. Does the corner of the window frame form a right triangle for the window to be rectangular?