Pythagorean Theorem and Distance Formula

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). Formula: a² + b² = c².

Tags

CCSS.8.G.B.8

Front

What is the Distance Formula?

Back

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

Tags

CCSS.HSG.GPE.B.7

Front

If a right triangle has legs of lengths 6 and 8, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(6² + 8²) = √(36 + 64) = √100 = 10.

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.

Tags

CCSS.4.G.A.2

Front

How can you determine if a triangle is a right triangle using side lengths?

Back

Use the Pythagorean Theorem: If a² + b² = c² holds true for the side lengths, then the triangle is a right triangle.

Tags

CCSS.8.G.B.8

Front

What is the hypotenuse in a right triangle?

Back

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

Front

Calculate the distance between the points (3, 4) and (7, 1).

Back

Using the Distance Formula: d = √((7 - 3)² + (1 - 4)²) = √(16 + 9) = √25 = 5.

Tags

CCSS.HSG.GPE.B.7

Front

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

Back

It is a right triangle because 3² + 4² = 5² (9 + 16 = 25).

Tags

CCSS.8.G.B.8

Front

If one leg of a right triangle is 12 and the hypotenuse is 13, what is the length of the other leg?

Back

Using the Pythagorean Theorem: b = √(13² - 12²) = √(169 - 144) = √25 = 5.

Tags

CCSS.8.G.B.7

Front

What is the formula to find the area of a right triangle?

Back

Area = (1/2) × base × height.

Tags

CCSS.6.G.A.1