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 the hypotenuse in a right triangle?

Back

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

Front

If a right triangle has sides of length 3 and 4, what is the length of the hypotenuse?

Back

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

Tags

CCSS.8.G.B.7

Front

True or False: The hypotenuse is always the longest side in a right triangle.

Back

True.

Front

What are the side lengths of a right triangle if the hypotenuse is 10 and one side is 6?

Back

The other side is 8 (Using the Pythagorean Theorem: 10² = 6² + b², so 100 = 36 + b², thus b² = 64, and b = 8).

Tags

CCSS.8.G.B.8

Front

Do the sides 5, 12, and 13 form a right triangle?

Back

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

Tags

CCSS.8.G.B.8

Front

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

Back

Use the Pythagorean Theorem: c² = a² + b², where c is the hypotenuse and a and b are the other two sides.

Tags

CCSS.8.G.B.8

Front

If a triangle has sides of lengths 7, 24, and 25, which side is the hypotenuse?

Back

25.

Tags

CCSS.8.G.B.8

Front

Can the sides 8, 15, and 20 form a right triangle?

Back

No (8² + 15² = 64 + 225 = 289, and 20² = 400).

Tags

CCSS.8.G.B.8

Front

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

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Tags

CCSS.8.G.B.8