Pythagorean Review 2

Front

What is a Pythagorean Triple?

Back

A set of three positive integers a, b, and c that satisfy the equation a² + b² = c².

Front

Does the set of numbers 10, 24, 26 represent a Pythagorean Triple?

Back

Yes, because 10² + 24² = 100 + 576 = 676 = 26².

Front

What is the Pythagorean Theorem?

Back

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): c² = a² + b².

Front

Solve for c if a = 5 and b = 12.

Back

c = 13, because 5² + 12² = 25 + 144 = 169, and √169 = 13.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance d between two points (x1, y1) and (x2, y2) is d = √((x2 - x1)² + (y2 - y1)²).

Front

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

Back

10, because 6² + 8² = 36 + 64 = 100, and √100 = 10.

Front

What does it mean if two triangles are similar?

Back

Two triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.

Front

What is the relationship between the areas of the squares on the sides of a right triangle?

Back

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

Front

Find the distance between points J(1, 2) and K(4, 6).

Back

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

Front

What is the formula for finding the area of a square?

Back

Area = side².