Pythagorean Theorem Practice

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 the formula to find the distance between two points (x1, y1) and (x2, y2)?

Back

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

Front

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

Back

Using the Pythagorean Theorem: c² = 3² + 4² = 9 + 16 = 25, so c = √25 = 5 units.

Front

What is the length of the missing side if one side is 6 units and the hypotenuse is 10 units?

Back

Using the Pythagorean Theorem: 10² = 6² + b², so 100 = 36 + b², thus b² = 64, and b = √64 = 8 units.

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. The shortest side is opposite the 30° angle.

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.

Front

How do you calculate the diagonal of a rectangle with width w and height h?

Back

The diagonal d can be calculated using the formula: d = √(w² + h²).

Front

If a laptop screen has a width of 10 inches and a height of 8 inches, what is the diagonal size?

Back

Using the formula: d = √(10² + 8²) = √(100 + 64) = √164 ≈ 12.81 inches, rounded to 13 inches.

Front

What is the significance of the hypotenuse in a right triangle?

Back

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

Front

What is the first step in solving a problem using the Pythagorean Theorem?

Back

Identify the lengths of the two legs of the right triangle and the hypotenuse.