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 lengths 6 and 8, what is the length of the hypotenuse?

Back

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

Tags

CCSS.8.G.B.7

Front

How do you 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

What is the formula to calculate the distance between two points in a coordinate plane?

Back

The distance formula is: d = √((x2 - x1)² + (y2 - y1)²).

Tags

CCSS.HSG.GPE.B.7

Front

In a right triangle, if one side is 3 and the hypotenuse is 5, what is the length of the other side?

Back

4 (Using the Pythagorean Theorem: 5² = 3² + b², 25 = 9 + b², b² = 16, b = 4).

Tags

CCSS.8.G.B.7

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.

Tags

CCSS.HSG.CO.C.10

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Tags

CCSS.8.G.B.8

Front

If a right triangle has a hypotenuse of 13 and one side of 5, what is the length of the other side?

Back

12 (Using the Pythagorean Theorem: 13² = 5² + b², 169 = 25 + b², b² = 144, b = 12).

Tags

CCSS.8.G.B.7

Front

What is the significance of the Pythagorean Theorem in real life?

Back

The Pythagorean Theorem is used in various fields such as construction, navigation, and physics to calculate distances and angles.

Tags

CCSS.8.G.B.8