9.3 Converse of the Pythagorean Theorem

Question 0

can you replace “longest side” with “hypotenuse” in the converse of the Pythagorean Theorem?

Answer 0

no because you don’t know if it’s a right triangle so you can’t use that word

Question 1

Converse of the Pythagorean Theorem

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Answer 1

if the square of the length of the LONGEST SIDE of a triangle is EQUAL to the sum of the squares of the lengths of the TWO SHORTER SIDES, then the triangle is a RIGHT TRIANGLE

• l^2 = s^2+m^2 —–> right triangle

Question 2

if the square of the length of the LONGEST SIDE of a triangle is LESS THAN the sum of the squares of the lengths of the TWO SHORTER SIDES, then…

*equation

Answer 2

the triangle is ACUTE

• l^2 < s^2+m^2 —–> acute triangle

Question 3

if the square of the length of the LONGEST SIDE of a triangle is GREATER THAN the sum of the squares of the lengths of the TWO SHORTER SIDES, then…

*equation

Answer 3

the triangle is OBTUSE

• l^2 > s^2+m^2 —–> obtuse triangle