Geometry

Geometry measures shapes and space. These articles cover angle facts, why a triangle's angles sum to 180°, the Pythagorean theorem, area, perimeter and volume formulae, circles and the number pi, and how coordinates turn distance and circles into algebra.

Angles Explained: Types of Angles and Angle Facts
An angle measures an amount of turn. A full turn is $360°$ , a straight line $180°$ and a right angle $90°$ . Angles on a straight line add to $180°$ and angles around a point add to $360°$ .
Why Do the Angles in a Triangle Add Up to 180°?
The three interior angles of any triangle add up to $180°$ . Isosceles triangles have two equal angles; equilateral triangles have three, each $60°$ .
The Pythagorean Theorem Explained: a² + b² = c²
In a right-angled triangle, the square of the hypotenuse (the longest side, opposite the right angle) equals the sum of the squares of the other two sides: $a^2 + b^2 = c^2$ .
Area and Perimeter: Formulas for Rectangles, Triangles and Trapeziums
Perimeter is the distance around the edge of a shape, measured in units. Area is the amount of surface it covers, measured in square units.
Circles and Pi: Circumference and Area of a Circle
For every circle, the circumference divided by the diameter is the same number, pi ( $\pi \approx 3.14159$ ). So the circumference is $C = 2\pi r$ and the area is $A = \pi r^2$ .
Volume and Surface Area of Prisms, Cylinders, Cones and Spheres
Volume is the space a solid takes up, in cubic units. For any prism or cylinder it is the cross-sectional area times the length; cones and pyramids hold exactly one third of that.
Distance and Midpoint Formulas and the Equation of a Circle
The distance formula $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ is Pythagoras on a grid. The midpoint averages the coordinates. A circle with centre $(h, k)$ and radius $r$ has equation $(x - h)^2 + (y - k)^2 = r^2$ .