Pythagorean Theorem w/ converse, triples, and inequalities

Pythagorean Theorem

• converse of Pythagorean theorem

• ​Pythagorean triples

• ​Pythagorean inequality theorem

​Pythagorean Theorem

Multiple Choice

A triangle has side lengths 3, 4, and 5.

Is this a right triangle?

• Yes, because $$3^2+4^2=5^2$$  

• No, because $$3^2+4^2\ne5^2$$  

​Pythagorean Triples

As we discovered on slides 2 and 3, a triangle with side lengths 3, 4, and 5 is a right triangle.

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​The set of numbers [3, 4, 5] is therefore a Pythagorean Triple.

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​Any set of whole numbers that satisfies the Pythagorean Theorem is considered a Pythagorean Triple.

Multiple Choice

A triangle has side lengths 8, 9, and 10.

Is this a right triangle?

• Yes, because $$8^2+9^2=10^2$$  

• No, because $$8^2+9^2\ne10^2$$  

Multiple Choice

Is the set of numbers [8, 9, 10] a Pythagorean Triple?

• Yes, because 8, 9, and 10 satisfy the Pythagorean Theorem

• No, because 8, 9, and 10 do not satisfy the Pythagorean Theorem

​Pythagorean Inequality Theorem

Multiple Choice

Which type of triangle will be created if you use side lengths 6, 8, and 9?

• right

• obtuse

• acute

Multiple Choice

Which type of triangle will be created if you use side lengths 6, 8, and 10?

• right

• obtuse

• acute

Multiple Choice

Which type of triangle will be created if you use side lengths 6, 8, and 11?

• right

• obtuse

• acute