Pythagorean Review 2

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: a² + b² = c².

Tags

CCSS.8.G.B.8

Front

How do you calculate the distance between two points (x1, y1) and (x2, y2)?

Back

The distance can be calculated using the distance formula: d = √((x2 - x1)² + (y2 - y1)²).

Tags

CCSS.HSG.GPE.B.7

Front

What are the side lengths of a right triangle?

Back

A right triangle has one angle that measures 90 degrees. The side opposite the right angle is called the hypotenuse, while the other two sides are called the legs.

Front

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

Back

Yes, it is a right triangle because 3² + 4² = 5² (9 + 16 = 25).

Tags

CCSS.8.G.B.8

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 equals the square of the length of the hypotenuse.

Tags

CCSS.8.G.B.8

Front

Can the lengths 8, 15, and 17 form a right triangle?

Back

Yes, because 8² + 15² = 17² (64 + 225 = 289).

Tags

CCSS.8.G.B.8

Front

What is the formula to find the hypotenuse of a right triangle?

Back

The formula is c = √(a² + b²), where c is the hypotenuse and a and b are the lengths of the other two sides.

Tags

CCSS.8.G.B.8

Front

If a triangle has sides of lengths 4, 5, and 6, is it a right triangle?

Back

No, it is not a right triangle because 4² + 5² ≠ 6² (16 + 25 ≠ 36).

Tags

CCSS.8.G.B.8

Front

What is the distance between points (1, 2) and (4, 6)?

Back

The distance is 5 units, calculated as d = √((4 - 1)² + (6 - 2)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Tags

CCSS.HSG.GPE.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 determine distances and relationships between different points.

Tags

CCSS.8.G.B.8