Pythagorean Theorem and Special Right Triangle

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 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 shortest side (opposite the 30° angle) is 'x', the longer leg (opposite the 60° angle) is 'x√3', and the hypotenuse is '2x'.

Front

What are the side lengths of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the sides are in the ratio 1 : 1 : √2. Both legs are of equal length 'x', and the hypotenuse is 'x√2'.

Front

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

Back

To determine if a set of numbers can form a right triangle, check if the square of the largest number equals the sum of the squares of the other two numbers (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 is the relationship between the sides of a right triangle?

Back

In a right triangle, the side opposite the right angle is the hypotenuse, and it is the longest side. The other two sides are called the legs.

Front

If one leg of a 30-60-90 triangle is 4 cm, what is the length of the hypotenuse?

Back

The hypotenuse is 8 cm (4 cm multiplied by 2).

Front

If the lengths of the sides of a triangle are 5, 12, and 13, does it form a right triangle?

Back

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

Front

What is the formula to find the length of the missing side in a right triangle?

Back

Use the Pythagorean Theorem: c² = a² + b², where c is the hypotenuse and a and b are the other two sides.

Front

Can a triangle with sides 15, 12, and 9 exist?

Back

Yes, it can exist because the sum of the lengths of any two sides is greater than the length of the third side.