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.

Tags

CCSS.8.G.B.8

Front

What is a right triangle?

Back

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

Tags

CCSS.4.G.A.2

Front

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

Back

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

Tags

CCSS.8.G.B.7

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, where c is the longest side.

Tags

CCSS.8.G.B.8

Front

What is the formula to find the length of one side of a right triangle if the other two sides are known?

Back

To find the length of one side, rearrange the Pythagorean Theorem: a = √(c² - b²) or b = √(c² - a²).

Tags

CCSS.8.G.B.8

Front

What is the relationship between the sides of a 5-12-13 triangle?

Back

The sides 5, 12, and 13 form a right triangle because 5² + 12² = 25 + 144 = 169 = 13².

Tags

CCSS.8.G.B.8

Front

Can the sides 8, 10, and 12 form a right triangle?

Back

No, because 8² + 10² = 64 + 100 = 164, which is not equal to 12² (144).

Tags

CCSS.8.G.B.8

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance between two points (x₁, y₁) and (x₂, y₂) in a coordinate plane is given by d = √((x₂ - x₁)² + (y₂ - y₁)²).

Tags

CCSS.HSG.GPE.B.7

Front

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

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle, and is crucial for applying the Pythagorean Theorem.

Tags

CCSS.8.G.B.8

Front

What is the square of the hypotenuse in a right triangle with legs of length 6 and 8?

Back

c² = 6² + 8² = 36 + 64 = 100, so c = √100 = 10.

Tags

CCSS.8.G.B.8