Pythagorean Theorem Activity by Tony Ellison

What is the formula for the Pythagorean Theorem?

• a + b = c

• 2a + 2b = 2c

• a^2 - b^2 = c^2

• a^2 + b^2 = c^2

In a right triangle, which side is considered the hypotenuse?

• The side opposite the acute angle

• The side adjacent to the right angle

• The longest side of the triangle

• The side opposite the right angle

If the two legs of a right triangle are 3 and 4 units long, what is the length of the hypotenuse?

• 7

• 6

• 8

• 5

What is the Pythagorean triple for a right triangle with sides 5, 12, and 13?

• 3, 4, 5

• 7, 24, 25

• 8, 15, 17

• 5, 12, 13

How can the Pythagorean Theorem be used to find the distance between two points on a coordinate plane?

• distance = sqrt((x2 - x1) * (y2 - y1))

• distance = (x2 - x1) + (y2 - y1)

• distance = (x2 - x1) - (y2 - y1)

• distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

If the hypotenuse of a right triangle is 10 units long and one leg is 6 units long, what is the length of the other leg?

• 12

• 4

• 5

• 8

Explain how the Pythagorean Theorem can be applied in real-life situations.

• By using the formula a^2 + b^2 = c^2, where 'a' and 'b' are the lengths of the two shorter sides of a right triangle, and 'c' is the length of the hypotenuse.

• The Pythagorean Theorem is only applicable in theoretical mathematics

• The Pythagorean Theorem is only relevant for equilateral triangles

• The Pythagorean Theorem can be used to calculate the area of a circle

What is the relationship between the squares of the two legs of a right triangle and the square of the hypotenuse?

• a^2 = b^2 = c^2

• a^2 * b^2 = c^2

• a^2 - b^2 = c^2

• The relationship between the squares of the two legs of a right triangle and the square of the hypotenuse is a^2 + b^2 = c^2, where a and b are the lengths of the legs, and c is the length of the hypotenuse.

If a ladder is leaning against a wall forming a right triangle with the ground, and the ladder is 15 feet long while the base of the ladder is 9 feet away from the wall, how high up the wall does the ladder reach?

• 12 feet

• 16 feet

• 14 feet

• 10 feet

Why is the Pythagorean Theorem important in the field of mathematics and beyond?

• The Pythagorean Theorem is important because it was discovered by Pythagoras himself

• The Pythagorean Theorem is important due to its fundamental relationship between the sides of a right triangle, enabling calculations in various fields beyond mathematics.

• The Pythagorean Theorem is crucial for solving algebraic equations

• The Pythagorean Theorem is significant due to its application in chemistry