Pythagorean Review 2

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

How do you find the length of the hypotenuse in a right triangle?

Back

To find the length of the hypotenuse in a right triangle, use the Pythagorean Theorem: c = √(a² + b²), where c is the hypotenuse and a and b are the lengths of the other two sides.

Tags

CCSS.8.G.B.7

Front

What is the distance formula in a coordinate plane?

Back

The distance formula is used to determine the distance between two points (x₁, y₁) and (x₂, y₂) in a coordinate plane. It is given by: d = √((x₂ - x₁)² + (y₂ - y₁)²).

Tags

CCSS.HSG.GPE.B.7

Front

How do you calculate the diagonal of a rectangle?

Back

To calculate the diagonal of a rectangle, use the Pythagorean Theorem: d = √(length² + width²), where d is the diagonal, length is the longer side, and width is the shorter side.

Tags

CCSS.8.G.B.7

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees. The side opposite the right angle is called the hypotenuse.

Front

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

Back

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

Tags

CCSS.8.G.B.8

Front

How can the Pythagorean Theorem be applied in real-life situations?

Back

The Pythagorean Theorem can be applied in various real-life situations, such as determining the length of a ladder needed to reach a certain height, calculating distances in navigation, and in construction to ensure structures are level.

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 side opposite the 30-degree angle is the shortest, the side opposite the 60-degree angle is √3 times the shortest side, and the hypotenuse is twice the shortest 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 solve for a missing side in a right triangle?

Back

To solve for a missing side in a right triangle, identify which sides are known and apply the Pythagorean Theorem: a² + b² = c², solving for the unknown side.

Tags

CCSS.8.G.B.7