The converse of a conditional switches the hypothesis and the conclusion. Sometimes
the converse of a true conditional is not true.
You can write the Pythagorean Theorem as a conditional: "If a triangle is a right triangle
with legs of lengths a and b and hypotenuse of length c, then a2 + b2 = c2.” The
converse of the Pythagorean Theorem is always true.Pr o p er t y The Converse of the Pyt hagorean Theorem
If a triangle has sides of lengths a, b, and c, and a2 + b2 = c2, then the triangle is a right
triangle with hypotenuse of length c.Why should you
check each answ er
choice?
If you find tw o answer
choices th a t appear to be
correct, then you know
you have made a mistake.
You can use the Pythagorean Theorem and its converse to determine whether a triangle
is a right triangle. If the side lengths satisfy the equation a2 + b2 = c2, then the triangle
is a right triangle. If they do not, then it is not a right triangle.Identifying Right Triangles
Multiple Choice Which set of lengths could be the side lengths of a right triangle?
(X > 6 in., 24 in., 25 in. ( D 4m,8m, 10 m C O 10 in., 24 in., 26 in. C O 8 ft, 15 ft, 16 ft
Determine whether the lengths satisfy a2 + b2 - c2. The greatest length is c.
62 + 242 ± 252 42 + 82 — 102 1 02 + 242 =*= 262 82 + 152 = 162
36 + 576 * 625 16 + 64 = 100 100 + 576 ± 676 64 + 225 = 256
612 + 625 80 * 100 676 = 676 289 * 256
By the Converse of the Pythagorean Theorem, the lengths 10 in., 24 in., and 26 in. could
be the side lengths of a right triangle. The correct answer is C.<§ Got It? 3. a. Could the lengths 20 mm, 47 mm, and 52 mm be the side lengths of a
right triangle? Explain,
b. Reasoning If a, b, and c satisfy the equation a 2 + b2 = c2, are 2a, 2b,
and 2c also possible side lengths of a right triangle? How do you know?Lesso n Ch eck
Do yo u k n o w H OW?
Find each missing side length.- Could the lengths 12 cm, 35 cm, and 37 cm be the
side lengths of a right triangle? Explain.
— - MATHEMAIICAL
Do y o u UN DERSTAN D? Jg j J PRACTICES- Vocabulary What is the converse of the conditional,
"If you study math, then you are a student”? - Error Analysis A student
found the length x in the
triangle at the right by solving
the equation 122 + 132 = x2.
Describe and correct the error.
616 Ch ap t er 10 Rad i cal Exp r essi o n s and Eq u at i o n s