Pythagorean Theorem Basics

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 is the hypotenuse of a right triangle?

Back

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

Front

In a right triangle, which angle is the right angle?

Back

The right angle is the angle that measures 90 degrees.

Front

To which type of triangles does the Pythagorean theorem apply?

Back

The Pythagorean theorem applies only to right triangles.

Front

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

Back

Using the Pythagorean theorem: 3² + 4² = c²; 9 + 16 = c²; 25 = c²; c = 5.

Front

True or False: The hypotenuse can be shorter than either leg of a right triangle.

Back

False. The hypotenuse is always the longest side of a right triangle.

Front

What is the formula to find the length of one leg of a right triangle if the hypotenuse and the other leg are known?

Back

If c is the hypotenuse and b is the known leg, the formula is: a = √(c² - b²).

Front

If the hypotenuse of a right triangle is 10 and one leg is 6, what is the length of the other leg?

Back

Using the formula: a = √(10² - 6²) = √(100 - 36) = √64 = 8.

Front

What is the relationship between the sides of a 3-4-5 triangle?

Back

In a 3-4-5 triangle, the lengths of the sides are in the ratio 3:4:5, which satisfies the Pythagorean theorem.

Front

What does it mean for a triangle to be a right triangle?

Back

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