Understand and Apply the 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 is expressed as: a² + b² = c².

Front

What is the formula to find the length of the hypotenuse in a right triangle?

Back

The formula to find the length of the hypotenuse (c) is: c = √(a² + b²).

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

The length of the hypotenuse is 5 units, calculated as: c = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What does it mean for a triangle to be a right triangle?

Back

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

Front

Can the Pythagorean Theorem be used for non-right triangles?

Back

No, the Pythagorean Theorem only applies to right triangles.

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Front

If a triangle has sides of lengths 5, 12, and 13, is it a right triangle?

Back

Yes, it is a right triangle because 5² + 12² = 13² (25 + 144 = 169).

Front

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

Back

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

Front

How do you determine if a triangle with sides 7, 24, and 25 is a right triangle?

Back

Check if 7² + 24² = 25². Since 49 + 576 = 625, it is a right triangle.

Front

What is the Pythagorean triple?

Back

A Pythagorean triple consists of three positive integers a, b, and c, such that a² + b² = c². Example: (3, 4, 5).