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 a right triangle?

Back

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

Front

What are the sides of a right triangle called?

Back

The sides of a right triangle are called the legs (the two shorter sides) and the hypotenuse (the longest side opposite the right angle).

Front

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

Back

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

Front

How do you find the length of the diagonal of a rectangle?

Back

Use the Pythagorean Theorem: diagonal² = length² + width².

Front

What is the hypotenuse in a right triangle?

Back

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

Front

If the hypotenuse is 13 units and one leg is 5 units, how do you find the other leg?

Back

Use the Pythagorean Theorem: leg² = hypotenuse² - other leg²; leg² = 13² - 5² = 169 - 25 = 144; leg = 12 units.

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 formula to calculate the area of a right triangle?

Back

Area = (1/2) × base × height.

Front

How can the Pythagorean Theorem be applied in real life?

Back

It can be used in construction, navigation, and various fields to determine distances and heights.