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). It can be expressed as: c² = a² + b².

Front

If a right triangle has legs of lengths 3 and 4, what is the length of the hypotenuse?

Back

5 (Using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25, so c = √25 = 5).

Front

What is a right triangle?

Back

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

Front

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

Back

Use the Pythagorean Theorem: If a² + b² = c² holds true for the lengths, then they can form a right triangle.

Front

What is the hypotenuse in a right triangle?

Back

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

Front

If one leg of a right triangle is 6 and the hypotenuse is 10, what is the length of the other leg?

Back

8 (Using the Pythagorean Theorem: 6² + b² = 10², so 36 + b² = 100, thus b² = 64, and b = 8).

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance between two points (x₁, y₁) and (x₂, y₂) in a coordinate plane is given by: d = √((x₂ - x₁)² + (y₂ - y₁)²).

Front

In a right triangle, if one leg is 12 and the hypotenuse is 13, what is the length of the other leg?

Back

5 (Using the Pythagorean Theorem: 12² + b² = 13², so 144 + b² = 169, thus b² = 25, and b = 5).

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.