Pythagorean Theorem 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). Formula: a² + b² = c².

Front

What are the legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle. They are usually referred to as 'a' and 'b' in the Pythagorean Theorem.

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle. It is denoted as 'c' in the Pythagorean Theorem.

Front

If a = 3 and b = 4, what is c?

Back

c = 5 (Using the Pythagorean Theorem: 3² + 4² = c², so 9 + 16 = c², thus c = 5).

Front

Is a triangle with sides 5, 12, and 13 a right triangle?

Back

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

Front

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

Back

In a right triangle, the sum of the squares of the two legs equals the square of the hypotenuse (a² + b² = c²).

Front

If a = 6 and c = 10, what is b?

Back

b = 8 (Using the Pythagorean Theorem: 6² + b² = 10², so 36 + b² = 100, thus b = 8).

Front

What does it mean if a triangle does not satisfy the Pythagorean Theorem?

Back

If a triangle does not satisfy the Pythagorean Theorem, it is not a right triangle.

Front

Can the lengths of the sides of a triangle be 7, 24, and 25?

Back

Yes, they can form a right triangle (7² + 24² = 25², so 49 + 576 = 625).

Front

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

Back

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