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 are the sides of a right triangle?

Back

In a right triangle, the two shorter sides are called the legs (a and b), and the longest side opposite the right angle is called the hypotenuse (c).

Front

How can you determine if a set of three lengths can form a right triangle?

Back

To determine if three lengths can form a right triangle, check if they satisfy the Pythagorean Theorem: a² + b² = c², where c is the longest side.

Tags

CCSS.8.G.B.8

Front

What is the length of the hypotenuse if the legs are 3 cm and 4 cm?

Back

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

Tags

CCSS.8.G.B.7

Front

If one leg of a right triangle is 5 cm and the hypotenuse is 13 cm, what is the length of the other leg?

Back

Using the Pythagorean Theorem: a² + 5² = 13². Thus, a² + 25 = 169, so a² = 144, and a = √144 = 12 cm.

Tags

CCSS.8.G.B.7

Front

What is a Pythagorean triple?

Back

A Pythagorean triple consists of three positive integers a, b, and c that satisfy the Pythagorean Theorem: a² + b² = c². An example is (3, 4, 5).

Tags

CCSS.8.G.B.8

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2. The shortest side is opposite the 30° angle, the longer leg is opposite the 60° angle, and the hypotenuse is the longest side.

Tags

CCSS.HSG.CO.C.10

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Tags

CCSS.8.G.B.8

Front

How do you find the area of a right triangle?

Back

The area of a right triangle can be found using the formula: Area = (1/2) × base × height.

Tags

CCSS.6.G.A.1

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 can be calculated using the formula: Distance = √((x₂ - x₁)² + (y₂ - y₁)²).

Tags

CCSS.HSG.GPE.B.7