100 cards
Geometry begins with a handful of fundamental ideas that describe the space around us. A point is the simplest of these: it represents a single location in space but has no size, no width, no length, and no depth. Because points have no dimensions, we represent them visually with dots and label them with capital letter...
An angle is formed wherever two rays share a common endpoint, called the vertex, and angles are measured in degrees based on the amount of rotation between them. The basic types describe where the angle falls on the 0° to 180° scale. An acute angle measures greater than 0° and less than 90°, with familiar examples incl...
Triangles are among the most studied shapes in geometry, and they can be sorted in two main ways. Classified by side length, an equilateral triangle has all three sides equal, an isosceles triangle has exactly two sides equal, and a scalene triangle has no equal sides. Each side classification carries angle consequence...
The most famous result in all of geometry applies specifically to right triangles. The Pythagorean Theorem states that in any right triangle with legs of length a and b and hypotenuse of length c, the equation a² + b² = c² holds true. The hypotenuse is the side opposite the right angle, and it is always the longest sid...
A circle is the set of all points in a plane that are the same distance, called the radius, from a central point. The distance across the circle through the center is called the diameter and equals twice the radius. The circumference, or distance around the circle, is given by C = 2πr or equivalently C = πd. The area e...
A regular polygon is a polygon with all sides equal in length and all interior angles equal in measure. Common examples include equilateral triangles, squares, and regular hexagons. The sum of the interior angles of any polygon with n sides is given by (n − 2) × 180°, so a hexagon with 6 sides has interior angles summi...
Coordinate geometry connects algebra and geometry by placing points on a grid. The distance between two points (x₁, y₁) and (x₂, y₂) is given by d = √[(x₂ − x₁)² + (y₂ − y₁)²], a formula derived directly from the Pythagorean Theorem. The midpoint of a segment with these endpoints is M = ((x₁ + x₂)/2, (y₁ + y₂)/2), whic...