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 can be expressed as: c² = a² + b².

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

Back

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

Front

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

Back

To find a missing side, rearrange the Pythagorean Theorem: a² = c² - b² or b² = c² - a².

Front

In a right triangle, if the hypotenuse is 10 units and one side is 6 units, what is the length of the other side?

Back

8 units (using the Pythagorean Theorem: 10² - 6² = 100 - 36 = 64, so the other side is √64 = 8).

Front

What is a right triangle?

Back

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

Front

How do you identify the sides of a right triangle?

Back

The sides are identified as the two legs (a and b) and the hypotenuse (c), where c is opposite the right angle.

Front

If the lengths of the two legs of a right triangle are equal, what type of triangle is it?

Back

It is an isosceles right triangle.

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.