Pythagorean Theorem Explained

The Pythagorean Theorem is named after which ancient figure?

• Euclid

• Archimedes

• Pythagoras

• Aristotle

What is the correct formula for the Pythagorean Theorem?

• a + b = c

• a^2 + b^2 = c^2

• a^2 - b^2 = c^2

• a + b = c^2

What is a defining characteristic of a right triangle?

• All angles are equal.

• It has one angle greater than 90 degrees.

• It has one angle equal to 90 degrees.

• All sides are equal.

In a right triangle, what is the longest side called and where is it located?

• Leg, adjacent to the right angle.

• Hypotenuse, opposite the right angle.

• Base, at the bottom of the triangle.

• Altitude, from a vertex to the opposite side.

A triangle has side lengths 3, 4, and 5. Is it a right triangle?

• Yes, because 3^2 + 4^2 = 5^2

• No, because 3 + 4 is not equal to 5

• Yes, because the sides are consecutive integers

• No, because the sum of the squares of the two shorter sides is not equal to the square of the longest side

What type of triangle must be used when applying the Pythagorean Theorem?

• Equilateral triangle

• Isosceles triangle

• Scalene triangle

• Right triangle

A right triangle has legs of length 5 and 12. What is the length of its hypotenuse?

• 17

• 13

• 169

• 7

For a right triangle with a hypotenuse of 10 and one leg of 8, which equation correctly represents the Pythagorean Theorem to find the missing leg (b)?

• 8^2 + b^2 = 10^2

• 10^2 + 8^2 = b^2

• b^2 - 8^2 = 10^2

• 10^2 - b^2 = 8^2

What is the inverse operation used to find the value of a variable when it is squared?

• Addition

• Subtraction

• Multiplication

• Taking the square root

In a right triangle, if one leg is 8 and the hypotenuse is 10, what is the length of the other leg?

• 6

• 8

• 10

• 36