Pythagorean Theorem and Converse

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 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 do you determine if three side lengths can form a right triangle?

Back

To determine if three side lengths can form a right triangle, check if the square of the longest side is equal to the sum of the squares of the other two sides (c² = a² + b²).

Tags

CCSS.8.G.B.8

Front

If a = 3 and b = 4, what is c?

Back

c = 5 (using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25, so c = √25 = 5).

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 a² + b² = c² for three sides, then the triangle is a right triangle.

Tags

CCSS.8.G.B.8

Front

If a = 6 and b = 8, does c = 10 form a right triangle?

Back

Yes, because 6² + 8² = 36 + 64 = 100, and 10² = 100.

Tags

CCSS.8.G.B.8

Front

What is the length of the hypotenuse if a = 12 and b = 16?

Back

c = 20 (using the Pythagorean Theorem: 12² + 16² = 144 + 256 = 400, so c = √400 = 20).

Tags

CCSS.8.G.B.8

Front

What is the length of one leg if the hypotenuse is 13 and the other leg is 5?

Back

The length of the leg is 12 (using the Pythagorean Theorem: 13² - 5² = 169 - 25 = 144, so leg = √144 = 12).

Tags

CCSS.8.G.B.7

Front

What is the distance between points (3, 4) and (0, 0)?

Back

The distance is 5 (using the distance formula: √((3-0)² + (4-0)²) = √(9 + 16) = √25 = 5).

Tags

CCSS.HSG.GPE.B.7

Front

If a triangle has sides of lengths 7, 24, and 25, is it a right triangle?

Back

Yes, because 7² + 24² = 49 + 576 = 625, and 25² = 625.

Tags

CCSS.8.G.B.8