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 is 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

If one side of a right triangle is 3 and the other side is 4, what is the length of the hypotenuse?

Back

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

Front

What are the side lengths of a 30-60-90 triangle?

Back

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

Front

What is the formula to find the area of a triangle?

Back

Area = 1/2 * base * height.

Front

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

Back

The sum of the squares of the two shorter sides equals the square of the longest side (hypotenuse).

Front

Which set of side lengths forms a right triangle? 50, 100, 110; 15, 20, 30; 30, 40, 50; 20, 30, 40?

Back

30, 40, 50 forms a right triangle.

Front

What is the length of the missing side if the other two sides are 10 and 12?

Back

The missing side is approximately 15.6 (Using the Pythagorean Theorem: 10² + 12² = c²; 100 + 144 = c²; c = √244 ≈ 15.6).

Front

What is the distance formula in a coordinate plane?

Back

Distance = √((x2 - x1)² + (y2 - y1)²).

Front

What is the definition of hypotenuse?

Back

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