Pythagorean Theorem & Converse Flashcard

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 do we call the longest side of a right triangle?

Back

The longest side of a right triangle is called the hypotenuse.

Front

What are the other two sides of a right triangle called?

Back

The other two sides of a right triangle are called the legs.

Front

If a triangle has sides of lengths 3, 4, and 5, does it form a right triangle?

Back

Yes, it forms a right triangle because 3² + 4² = 5² (9 + 16 = 25).

Front

How can you determine if three lengths can form a right triangle?

Back

To determine if three lengths can form a right triangle, check if the square of the longest length equals the sum of the squares of the other two lengths.

Front

What is the converse of the Pythagorean Theorem?

Back

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

Front

What is the relationship between the hypotenuse and the legs in a right triangle?

Back

The hypotenuse is always longer than either of the legs in a right triangle.

Front

Can the hypotenuse be one of the legs in a right triangle?

Back

No, the hypotenuse cannot be one of the legs; it is the side opposite the right angle.

Front

What is the formula to find the length of the hypotenuse?

Back

The formula to find the length of the hypotenuse (c) is c = √(a² + b²), where a and b are the lengths of the legs.