The 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.

Tags

CCSS.8.G.B.8

Front

What are the legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle. They are usually referred to as sides a and b.

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle, and is denoted as side c.

Front

If one leg of a right triangle is 6 units and the other leg is 8 units, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 6² + 8²; c² = 36 + 64; c² = 100; c = 10 units.

Tags

CCSS.8.G.B.7

Front

True or False: The hypotenuse is always the longest side in a right triangle.

Back

True.

Front

In the Pythagorean Theorem, what does 'c' represent?

Back

'c' represents the length of the hypotenuse in a right triangle.

Tags

CCSS.8.G.B.8

Front

If a right triangle has legs of lengths 3 and 4, what is the length of the hypotenuse?

Back

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

Tags

CCSS.8.G.B.7

Front

What is the relationship between the sides of a right triangle according to the Pythagorean Theorem?

Back

The sum of the squares of the lengths of the two legs (a and b) equals the square of the length of the hypotenuse (c).

Tags

CCSS.8.G.B.8

Front

If a ladder is placed 10 feet away from a wall and reaches a height of 25 feet, how long is the ladder?

Back

Using the Pythagorean Theorem: c² = 10² + 25²; c² = 100 + 625; c² = 725; c ≈ 26.93 feet.

Tags

CCSS.8.G.B.8

Front

True or False: The Pythagorean Theorem can only be used for right triangles.

Back

True.

Tags

CCSS.8.G.B.8