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

In the Pythagorean Theorem, what do the variables a, b, and c represent?

Back

In the Pythagorean Theorem, 'a' and 'b' represent the lengths of the two legs of a right triangle, while 'c' represents the length of the hypotenuse.

Tags

CCSS.8.G.B.8

Front

How do you calculate the length of the hypotenuse using the Pythagorean Theorem?

Back

To calculate the length of the hypotenuse (c), use the formula c = √(a² + b²), where a and b are the lengths of the other two sides.

Tags

CCSS.8.G.B.8

Front

If one leg of a right triangle is 6 units and the other leg is 8 units, what is the length of the hypotenuse?

Back

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

Tags

CCSS.8.G.B.7

Front

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

Back

In a right triangle, the sum of the squares of the lengths of the two legs (a and b) is equal to the square of the length of the hypotenuse (c): a² + b² = c².

Tags

CCSS.8.G.B.8

Front

Can the Pythagorean Theorem be used for non-right triangles?

Back

No, the Pythagorean Theorem only applies to right triangles.

Tags

CCSS.8.G.B.8

Front

What is the formula to find one leg of a right triangle if the hypotenuse and the other leg are known?

Back

If the hypotenuse (c) and one leg (a) are known, the other leg (b) can be found using the formula b = √(c² - a²).

Tags

CCSS.8.G.B.7

Front

If a ladder is placed 10 feet away from a wall and reaches a height of 25 feet, how long is the ladder?

Back

Using the Pythagorean Theorem: c = √(10² + 25²) = √(100 + 625) = √725 ≈ 26.93 feet.

Tags

CCSS.8.G.B.8

Front

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

Back

The Pythagorean Theorem is used in various real-life applications, such as construction, navigation, and physics, to determine distances and relationships between different points.

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 a triangle has sides of lengths a, b, and c, and if a² + b² = c², then the triangle is a right triangle.

Tags

CCSS.8.G.B.8