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: c² = a² + b².

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 legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle.

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

If one leg of a right triangle is 3 units and the other leg is 4 units, what is the length of the hypotenuse?

Back

Using the Pythagorean theorem: c² = 3² + 4²; c² = 9 + 16; c² = 25; c = 5 units.

Tags

CCSS.8.G.B.7

Front

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

Back

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

Tags

CCSS.8.G.B.8

Front

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

Back

To determine if three lengths can form a right triangle, check if the square of the longest length equals the sum of the squares of the other two lengths.

Tags

CCSS.8.G.B.8

Front

What is the distance formula derived from the Pythagorean theorem?

Back

The distance formula to find the distance between two points (x1, y1) and (x2, y2) is: d = √((x2 - x1)² + (y2 - y1)²).

Tags

CCSS.HSG.GPE.B.7

Front

What is an example of a real-world application of the Pythagorean theorem?

Back

An example is finding the shortest distance between two points on a map, such as the distance a plane travels when flying north and then east.

Tags

CCSS.8.G.B.8

Front

What type of angle is formed by the legs of a right triangle?

Back

The angle formed by the legs of a right triangle is a right angle (90 degrees).