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: c² = a² + b².

Front

What are the side lengths 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. The side opposite the 30° angle is the shortest (a), the side opposite the 60° angle is √3 times the shortest side (b), and the hypotenuse is twice the shortest side (c).

Front

How do you find the length of the hypotenuse in a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the length of the hypotenuse (c) is found by multiplying the length of one leg (a) by √2: c = a√2.

Front

Can the lengths 3, 4, and 9 form a triangle?

Back

No, the lengths 3, 4, and 9 cannot form a triangle because they do not satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side.

Front

What is the triangle inequality theorem?

Back

The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Front

In a right triangle, what is the relationship between the legs and the hypotenuse?

Back

In a right triangle, the hypotenuse is always the longest side, and its length is greater than the lengths of either leg.

Front

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

Back

The area (A) of a right triangle can be calculated using the formula: A = (1/2) * base * height.

Front

What is a leg in a right triangle?

Back

A leg in a right triangle refers to either of the two sides that form the right angle.

Front

What is the long leg in a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the long leg (b) is the side opposite the 60° angle and is √3 times the length of the shorter leg (a).

Front

What is the short leg in a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the short leg (a) is the side opposite the 30° angle.