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: a² + b² = c².

Tags

CCSS.8.G.B.8

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem only applies to right triangles.

Tags

CCSS.8.G.B.8

Front

What is the hypotenuse of a right triangle?

Back

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

Front

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

Back

Using the Pythagorean Theorem: 3² + 4² = c², which gives 9 + 16 = c², so c² = 25, thus c = 5.

Tags

CCSS.8.G.B.7

Front

Does the set of numbers 20, 25, and 15 represent a right triangle?

Back

Yes, because 20² + 15² = 400 + 225 = 625 = 25².

Tags

CCSS.8.G.B.8

Front

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

Back

To find a missing side, use the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse.

Tags

CCSS.8.G.B.7

Front

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

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Tags

CCSS.8.G.B.8

Front

What is the significance of the right angle in a right triangle?

Back

The right angle (90 degrees) is crucial because it allows the use of the Pythagorean Theorem to determine the relationship between the sides.

Tags

CCSS.8.G.B.8

Front

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

Back

No, the Pythagorean Theorem is specifically for right triangles.

Tags

CCSS.8.G.B.8

Front

What is the value of the hypotenuse if one leg is 6 and the other leg is 8?

Back

Using the Pythagorean Theorem: 6² + 8² = c², which gives 36 + 64 = c², so c² = 100, thus c = 10.

Tags

CCSS.8.G.B.7