Pythagorean Theorem Warm-Up

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

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

Back

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

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance between two points (x1, y1) and (x2, y2) in a coordinate plane is given by: d = √((x2 - x1)² + (y2 - y1)²).

Front

In a right triangle, if one leg is 5 units and the hypotenuse is 13 units, what is the length of the other leg?

Back

12 units (Using the Pythagorean Theorem: c² = a² + b² => 13² = 5² + b² => 169 = 25 + b² => b² = 144 => b = 12).

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, the longer leg is opposite the 60° angle, and the hypotenuse is twice the shortest side.

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 find the area of a right triangle?

Back

The area of a right triangle can be found using the formula: Area = (1/2) * base * height.

Front

If a ladder is placed 10 feet away from a wall and reaches a height of 24 feet, how long is the ladder?

Back

26 feet (Using the Pythagorean Theorem: c² = 10² + 24² => c² = 100 + 576 => c² = 676 => c = 26).

Front

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

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle, and is crucial for applying the Pythagorean Theorem.

Front

If a triangle has sides of lengths 7, 24, and 25, is it a right triangle?

Back

Yes, it is a right triangle (Using the Pythagorean Theorem: 25² = 7² + 24² => 625 = 49 + 576 => 625 = 625).