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: a² + b² = c².

Front

What is a right triangle?

Back

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

Front

What are Pythagorean Triples?

Back

Pythagorean Triples are sets of three positive integers (a, b, c) that satisfy the Pythagorean Theorem, meaning a² + b² = c². Examples include (3, 4, 5) and (5, 12, 13).

Front

How do you find the length of the hypotenuse in a right triangle?

Back

To find the length of the hypotenuse (c), use the formula: c = √(a² + b²), where a and b are the lengths of the other two sides.

Front

How do you find the length of a leg in a right triangle?

Back

To find the length of a leg (a or b), rearrange the Pythagorean Theorem: a = √(c² - b²) or b = √(c² - a²).

Front

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

Back

In a 3-4-5 triangle, the lengths of the sides are in the ratio 3:4:5, which satisfies the Pythagorean Theorem: 3² + 4² = 5².

Front

What is the formula to check if a triangle is a right triangle?

Back

To check if a triangle with sides a, b, and c is a right triangle, verify if a² + b² = c², where c is the longest side.

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

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

Back

No, the Pythagorean Theorem only applies to right triangles.

Front

What is the converse of the Pythagorean Theorem?

Back

The converse of the Pythagorean Theorem states that if a triangle has sides a, b, and c such that a² + b² = c², then the triangle is a right triangle.