8.GSR.8.2 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.

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

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 one leg of a right triangle is 3 and the other leg is 4, what is the length of the hypotenuse?

Back

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

Front

How do you find the area of a square?

Back

The area of a square is found by squaring the length of one of its sides: Area = side².

Front

What is the relationship between the areas of the squares on the legs of a right triangle and the area of the square on the hypotenuse?

Back

The sum of the areas of the squares on the two legs is equal to the area of the square on the hypotenuse.

Front

If a right triangle has legs of length 6 and 8, what is the area of the square on the hypotenuse?

Back

100 (Using the Pythagorean Theorem: 6² + 8² = 36 + 64 = 100).

Front

What is the formula to calculate the distance from a point to a line using the Pythagorean Theorem?

Back

The distance can be calculated using the formula: Distance = √(x² + y²), where x and y are the horizontal and vertical distances from the point to the line.

Front

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

Back

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

Front

If a ladder is leaning against a wall, how can you find the height it reaches?

Back

You can use the Pythagorean Theorem: height² + distance from the wall² = ladder length².