8th Grade Vocab: 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 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

What are the sides of a right triangle called?

Back

The sides of a right triangle are called the legs (the two shorter sides) and the hypotenuse (the longest side opposite the right angle).

Front

How do you find the length of the hypotenuse using the Pythagorean Theorem?

Back

To find the length of the hypotenuse, use the formula c = √(a² + b²), where a and b are the lengths of the legs.

Tags

CCSS.8.G.B.8

Front

What is the relationship between the sides of a 3-4-5 triangle?

Back

In a 3-4-5 triangle, the lengths of the sides are in the ratio 3:4:5, which satisfies the Pythagorean Theorem (3² + 4² = 5²).

Tags

CCSS.8.G.B.8

Front

What is an example of using the Pythagorean Theorem in real life?

Back

An example is determining the height of a ladder leaning against a wall. If the base of the ladder is 3 feet from the wall and the ladder is 5 feet long, you can find the height using the Pythagorean Theorem.

Tags

CCSS.8.G.B.8

Front

What is the converse of the Pythagorean Theorem?

Back

The converse of the Pythagorean Theorem states that if a triangle has sides of lengths a, b, and c, and a² + b² = c², then the triangle is a right triangle.

Tags

CCSS.8.G.B.8

Front

What is a perfect square?

Back

A perfect square is a number that can be expressed as the square of an integer. For example, 1, 4, 9, 16, and 25 are perfect squares.

Tags

CCSS.6.EE.A.1

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance formula, which calculates the distance between two points (x₁, y₁) and (x₂, y₂) in a coordinate plane, is: d = √((x₂ - x₁)² + (y₂ - y₁)²).

Tags

CCSS.HSG.GPE.B.7

Front

What is the significance of the Pythagorean Theorem in geometry?

Back

The Pythagorean Theorem is fundamental in geometry as it helps in calculating distances, constructing right angles, and solving various geometric problems.

Tags

CCSS.8.G.B.8