Pythagorean Triples

Front

What is a Pythagorean Triple?

Back

A Pythagorean Triple consists of three positive integers a, b, and c, such that a² + b² = c², where c is the hypotenuse of a right triangle.

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): a² + b² = c².

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem applies only to right triangles.

Front

How can you determine if a triangle is acute, obtuse, or right using side lengths?

Back

To determine the type of triangle, compare the square of the longest side (c) to the sum of the squares of the other two sides (a and b): If a² + b² > c², the triangle is acute; if a² + b² < c², it is obtuse; if a² + b² = c², it is right.

Front

What is the relationship between the sides of a 3-4-5 triangle?

Back

The sides of a 3-4-5 triangle are a Pythagorean Triple, satisfying the Pythagorean Theorem: 3² + 4² = 5².

Front

Can the lengths 15, 20, and 25 form a Pythagorean Triple?

Back

Yes, because 15² + 20² = 225 + 400 = 625 = 25².

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), where a and b are the lengths of the other two sides.

Front

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

Back

To find a missing side, rearrange the Pythagorean Theorem: a = √(c² - b²) or b = √(c² - a²), depending on which side is missing.

Front

What are some common Pythagorean Triples?

Back

Common Pythagorean Triples include (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25).

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.