Pythagorean Theorem Converse

What are the 2 shorter sides of a right triangle called?

• Legs

• Hypotenuse

• Angles

• Vertices

If a triangle has sides 8, 15, and 17, is it a right triangle?

• Yes, because 8² + 15² = 17².

• No, because the sides do not satisfy the Pythagorean theorem.

• Yes, because 8² + 15² > 17².

• No, because it is an obtuse triangle.

a = 2.1, b = 7.2, c = 7.5. Is this a right triangle?

• Yes

• No

• It depends on the angles

• Only if c is the longest side

Which set of side lengths does not form a right triangle? 14, 15, 29 or 38, 80, 90?

• 14, 15, 29

• 38, 80, 90

• 10, 24, 26

• 5, 12, 13

If a triangle has sides of lengths 5, 12, and 13, does it form a right triangle?

• Yes, because 5² + 12² = 13².

• No, because 5 + 12 is not greater than 13.

• Yes, because it has one angle of 90 degrees.

• No, because the sides do not satisfy the triangle inequality.

Do the segment lengths 9, 12, and 15 form a right triangle?

• Yes

• No

• Only two segments can form a right triangle

• The segments do not meet the triangle inequality

How can you determine if three lengths can form a right triangle?

• Check if a² + b² = c², where c is the longest side.

• Check if a + b = c, where c is the longest side.

• Check if a² - b² = c², where c is the longest side.

• Check if a + b > c, where c is the longest side.

What is the relationship between the sides of a right triangle?

• The sum of the squares of the two legs equals the square of the hypotenuse.

• The sum of the lengths of all three sides is equal to the length of the hypotenuse.

• The product of the two legs equals the length of the hypotenuse.

• The difference between the lengths of the two legs equals the length of the hypotenuse.

What is the Pythagorean Theorem?

• In a right triangle, a² + b² = c², where c is the hypotenuse.

• In any triangle, the sum of the angles equals 180 degrees.

• The area of a circle is πr².

• The square of the hypotenuse is equal to the sum of the squares of the other two sides.

What is a right triangle?

• A triangle with one angle measuring 90 degrees.

• A triangle with all angles measuring less than 90 degrees.

• A triangle with two equal sides and one angle measuring 60 degrees.

• A triangle with one angle measuring 180 degrees.