Pythagorean Theorem Review

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 type of triangle is formed when c² < a² + b²?

Back

Acute Triangle

Front

What type of triangle is formed when c² = a² + b²?

Back

Right Triangle

Front

What type of triangle is formed when c² > a² + b²?

Back

Obtuse Triangle

Front

If a = 3 and b = 4, what is c using the Pythagorean Theorem?

Back

c = 5 (since 3² + 4² = 9 + 16 = 25, and √25 = 5).

Front

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

Back

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

Front

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

Back

The distance is 5 (using the distance formula: d = √((4-1)² + (6-2)²) = √(3² + 4²) = √(9 + 16) = √25 = 5).

Front

What is the hypotenuse of a right triangle with legs of length 6 and 8?

Back

The hypotenuse is 10 (since 6² + 8² = 36 + 64 = 100, and √100 = 10).

Front

If the hypotenuse is 13 and one leg is 5, what is the length of the other leg?

Back

The other leg is 12 (using the Pythagorean Theorem: 13² = 5² + b², so 169 = 25 + b², thus b² = 144, and b = 12).

Front

What is the formula for finding the area of a right triangle?

Back

Area = (1/2) * base * height.