Pythagorean Theorem

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: c² = a² + b².

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

If one side of a right triangle is 3 units and the other side is 4 units, what is the length of the hypotenuse?

Back

5 units (using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).

Front

What are the lengths of the sides of a 5-12-13 triangle?

Back

The lengths of the sides are 5 units, 12 units, and 13 units, which form a right triangle.

Front

How do you determine if a triangle is a right triangle using side lengths?

Back

You can use the Pythagorean Theorem: if a² + b² = c² holds true for the side lengths, then the triangle is a right triangle.

Front

What is the length of the diagonal of a rectangle with a length of 40 yards and a width of 30 yards?

Back

50 yards (using the Pythagorean Theorem: √(40² + 30²) = √(1600 + 900) = √2500 = 50).

Front

What is the formula to find the length of the diagonal of a rectangle?

Back

The formula is: Diagonal = √(length² + width²).

Front

What is the relationship between the sides of a right triangle and the Pythagorean Theorem?

Back

The Pythagorean Theorem establishes a relationship between the lengths of the sides of a right triangle, specifically that the square of the hypotenuse equals the sum of the squares of the other two sides.

Front

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

Back

Yes, it is a right triangle because 8² + 15² = 64 + 225 = 289, and 17² = 289.

Front

What is the significance of the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.