Pythagorean Theorem and Converse Basics

What type of triangle is involved in the Pythagorean theorem?

• Equilateral triangle

• Isosceles triangle

• Scalene triangle

• Right triangle

What is the formula for the Pythagorean theorem?

• a^2 + b^2 = c^2

• 2ab = c^2

• a + b = c

• a^2 - b^2 = c^2

How do you solve for a missing side length in a right triangle using the Pythagorean theorem?

• Apply the Pythagorean theorem formula: a^2 + b^2 = c^2, where 'a' and 'b' are the known side lengths and 'c' is the hypotenuse. Solve for the missing side length by taking the square root of the result.

• Subtract the two known side lengths

• Multiply the two known side lengths

• Divide the two known side lengths

What is the Pythagorean Converse?

• A triangle is only a right triangle if the sum of the squares of the sides is less than the square of the longest side.

• The Pythagorean Converse states that all triangles are right triangles.

• If the sum of the squares of the sides of a triangle is not equal to the square of the longest side, then the triangle is a right triangle.

• If the square of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

A triangle has sides of lengths 9, 40, and 41. Using the converse of the Pythagorean theorem, determine if it is a right triangle.

• Yes

• No

Using the converse of the Pythagorean theorem, determine if the following triangle is a right triangle: sides are 21 cm, 28 cm, and 35 cm.

• Yes

• No

A triangle has sides of 6 cm, 8 cm, and 10 cm. Using the converse of the Pythagorean theorem, is this triangle a right triangle?

• Yes

• No

Do three squares with side lengths of 6, 12, and 13 form a right triangle?

• Yes

• No

If a triangle has side lengths of 7, 24, and 25, what can be said about the triangle?

• It is acute.

• It is obtuse.

• It is right.

• It is equilateral.