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 a² + b² = c².

Front

In a right triangle, which side is the hypotenuse?

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 and the other side is 4, what is the length of the hypotenuse?

Back

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

Front

What is the relationship between the sides of a right triangle?

Back

The relationship is defined by the Pythagorean Theorem: a² + b² = c².

Front

Can the Pythagorean Theorem be used for non-right triangles?

Back

No, the Pythagorean Theorem only applies to right triangles.

Front

If a = 6 and b = 8, what is c?

Back

10 (Using the Pythagorean Theorem: 6² + 8² = 36 + 64 = 100; √100 = 10).

Front

What are the conditions for a triangle to be a right triangle?

Back

A triangle is a right triangle if it satisfies the Pythagorean Theorem: a² + b² = c².

Front

Which of the following sets of numbers can form a right triangle: 5, 12, 13 or 7, 24, 25?

Back

Both sets can form right triangles (5² + 12² = 13² and 7² + 24² = 25²).

Front

What is the value of c if a = 9 and b = 40?

Back

41 (Using the Pythagorean Theorem: 9² + 40² = 81 + 1600 = 1681; √1681 = 41).

Front

Is the statement 'side a on a right triangle is ALWAYS the longest side' true or false?

Back

False. The longest side is always the hypotenuse, which is side c.