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 is expressed as c² = a² + b².

Tags

CCSS.8.G.B.8

Front

What are the sides of a right triangle called?

Back

In a right triangle, the two shorter sides are called '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 numbers can form a right triangle?

Back

To determine if three numbers can form a right triangle, check if the square of the largest number is equal to the sum of the squares of the other two numbers. If c² = a² + b² holds true, they can form a right triangle.

Tags

CCSS.8.G.B.8

Front

If the lengths of the legs of a right triangle are 3 and 4, what is the length of the hypotenuse?

Back

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

Tags

CCSS.8.G.B.7

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the relationship between the sides is defined by the Pythagorean Theorem: c² = a² + b².

Tags

CCSS.8.G.B.8

Front

Is the statement 'c² = a² - b²' true or false?

Back

False. The correct statement is c² = a² + b².

Tags

CCSS.8.G.B.8

Front

What is the value of the hypotenuse if one leg is 6 and the other leg is 8?

Back

Using the Pythagorean Theorem: c² = 6² + 8² = 36 + 64 = 100. Therefore, c = √100 = 10.

Tags

CCSS.8.G.B.7

Front

What does it mean for a triangle to be a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Tags

CCSS.4.G.A.2

Front

Can the lengths 5, 12, and 13 form a right triangle?

Back

Yes, because 13² = 5² + 12² (169 = 25 + 144).

Tags

CCSS.8.G.B.8

Front

What is the formula to find the length of a missing side in a right triangle?

Back

To find a missing side, rearrange the Pythagorean Theorem: c = √(a² + b²) for the hypotenuse, or a = √(c² - b²) and b = √(c² - a²) for the legs.

Tags

CCSS.8.G.B.7