Pythagorean Theorem & 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). It can be expressed as: c² = a² + b².

Tags

CCSS.8.G.B.8

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem only applies to right triangles.

Tags

CCSS.8.G.B.8

Front

If a triangle has sides of lengths 3, 4, and 5, is it a right triangle?

Back

Yes, because 3² + 4² = 5² (9 + 16 = 25).

Tags

CCSS.8.G.B.8

Front

Calculate the length of the hypotenuse for a right triangle with legs of 6 and 8.

Back

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

Tags

CCSS.8.G.B.7

Front

What is the converse of the Pythagorean Theorem?

Back

The converse 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

Determine if the sides 9, 12, and 15 form a right triangle.

Back

Yes, because 9² + 12² = 15² (81 + 144 = 225).

Tags

CCSS.8.G.B.8

Front

What is the length of the diagonal of a rectangle that is 50 yards wide and 100 yards long?

Back

Using the Pythagorean Theorem: c² = 50² + 100² = 2500 + 10000 = 12500, so c = √12500 ≈ 111.8 yards.

Tags

CCSS.8.G.B.8

Front

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

Back

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

Tags

CCSS.8.G.B.8

Front

What is the formula to find the length of one side of a right triangle if the other two sides are known?

Back

To find the length of one side, rearrange the Pythagorean Theorem: a = √(c² - b²) or b = √(c² - a²).

Tags

CCSS.8.G.B.8

Front

What are the three sides of a right triangle called?

Back

The three sides are called the legs (a and b) and the hypotenuse (c).