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

What are the sides of a right triangle called?

Back

The sides of a right triangle are called the legs (the two shorter sides) and the hypotenuse (the longest side opposite the right angle).

Front

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

Back

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

Front

Can the sides 10.5, 11.3, and 13.8 form a right triangle?

Back

No, they cannot form a right triangle because 10.5² + 11.3² ≠ 13.8².

Front

Can the sides 2.1, 3.5, and 2.8 form a right triangle?

Back

Yes, they can form a right triangle because 2.1² + 2.8² = 3.5².

Front

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

Back

The formula to find the diagonal (d) of a rectangle is d = √(length² + width²).

Front

If a rectangular picture has sides of 20 inches and 30 inches, what is the length of the diagonal?

Back

36.1 inches (Using the formula: d = √(20² + 30²) = √(400 + 900) = √1300 ≈ 36.1).

Front

In a right triangle, what is the hypotenuse?

Back

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

Front

If side a is 9 and side b is 6, what is the hypotenuse?

Back

10.8 (Using the Pythagorean Theorem: 9² + 6² = 81 + 36 = 117; √117 ≈ 10.8).