Pythagorean Flashcards

Pythagorean Flashcards Summary

• Right Angle: Measures 90 degrees; crucial in right triangles.

• Hypotenuse: The longest side of a right triangle, opposite the right angle.

• Right Triangle: Defined by having one right angle.

• Leg: In a right triangle, each of the two sides that together form the right angle.

• Pythagorean Theorem: Expressed as (a^2 + b^2 = c^2), where (c) is the hypotenuse, and (a) and (b) are the legs.

• Perfect Square Numbers: Numbers that can be represented as the square of an integer.

• Examples of Perfect Squares: Include 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, and 144.

• Irrational Numbers: Non-terminating, non-repeating decimals; cannot predict the next digit.

• Perimeter: The total distance around a geometric shape.

• Area: Represents the quantity of square units contained within a shape.

• Approximate Values: Indicate a close estimation rather than an exact figure.

• Exact Values: Denote precise measures without ambiguity.

• Exact Side Length Calculation: For a square with area 10, the side length is ( \sqrt{10} ).

• Approximate Side Length Calculation: For a square with area 10, approximately 3.162.

• Exact Side Length for Area 55: Calculated as ( \sqrt{55} ).

• Approximate Side Length for Area 55: Roughly 7.416.

• General Side Length Formula: For any square with area ( \otimes ), the side length is ( \sqrt{\otimes} ).

• Exact Side Length for Area 100: Precisely 10.

• Area Calculation Confirmation: Area of a square with side length 10 equals 100.

• Area of Square with Side ( \sqrt{10} ): Equals 10.

• Area Calculation for Side Length ( \otimes ): ( \otimes^2 ).

• Perimeter Example: A square with side length 5 has a perimeter of 20.

• Area Example: A square with side length 5 has an area of 25.

• Perimeter Example: For a square with side length 10, the perimeter is 40.

• Right Triangle Check: Sides of length 18, 24, and 30 satisfy the Pythagorean theorem, confirming a right triangle.

• Non-Right Triangle Check: Sides of 8, 72, and 75 do not satisfy the Pythagorean theorem.

• Midpoint Definition (General): A point dividing a line segment into two equal parts.

• Midpoint Formula (Math): ((x_1+x_2)/2, (y_1+y_2)/2).

• Midpoint Example: The midpoint of the segment from -3 to 10 is 3.5.

• Midpoint Example: The midpoint of the segment from -10 to -3 is -6.5.