Pythagorean Flashcards

Questions and Answers

What is a right angle?

An angle that measures 360 degrees

An angle that measures 90 degrees (correct)

An angle that measures 180 degrees

An angle that measures 45 degrees

What is the longest side of a right triangle called?

hypotenuse

What defines a right triangle?

A triangle with one right angle

What is a leg in a right triangle?

One side that forms the right angle Signup and view all the answers

What does the Pythagorean Theorem state?

The squares of the legs add to the square of the hypotenuse Signup and view all the answers

Which of the following are perfect square numbers?

1, 4, 9 Signup and view all the answers

What defines a number that is irrational?

A decimal that never ends and never repeats Signup and view all the answers

What is the perimeter of a square with side length 5?

20 Signup and view all the answers

What is the area of a square with side length 10?

100 Signup and view all the answers

What is the approximate side length of a square with area 10?

3.162 Signup and view all the answers

Can the lengths 18, 24, and 30 form a right triangle?

Yes Signup and view all the answers

Can the lengths 8, 72, and 75 form a right triangle?

No Signup and view all the answers

What is the midpoint of the line segment from -3 to 10?

3.5 Signup and view all the answers

What is the midpoint of the line segment from -10 to -3?

-6.5 Signup and view all the answers

Study Notes

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.

Description

Test your knowledge of key concepts related to right triangles with these flashcards. This quiz covers essential terms like right angle, hypotenuse, and the Pythagorean Theorem. Improve your understanding of geometry in a fun and engaging way!