Master geometry from basic angle relationships to 3D volume calculations with this comprehensive flashcard deck. Geometry is one of the oldest branches of mathematics and is heavily tested on the SAT, ACT, GCSE, A-Level, and state standardized exams. A strong...
Master geometry from basic angle relationships to 3D volume calculations with this comprehensive flashcard deck. Geometry is one of the oldest branches of mathematics and is heavily tested on the SAT, ACT, GCSE, A-Level, and state standardized exams. A strong geometry foundation is also essential for physics, architecture, engineering, and computer
graphics.
This deck covers all essential geometry formulas and theorems: angle types and relationships, triangle properties and congruence rules, the Pythagorean theorem, polygon properties, circle theorems, area and perimeter formulas, and 3D shape volumes and surface areas.
Based on publicly available educational resources including OpenStax Geometry and CK-12.
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Complementary: Two angles that add to 90°. Supplementary: Two angles that add to 180°. Memory trick: C comes before S in the alphabet, 90 comes before 180.
When two lines intersect, the angles directly across from each other are vertical angles — they are always equal. The adjacent angles are supplementary.
When a transversal crosses two parallel lines, alternate interior angles (on opposite sides of the transversal, between the parallel lines) are equal.
When a transversal crosses two parallel lines, co-interior angles (on the same side, between the parallel lines) are supplementary — they add up to 180°.
In a right triangle: a² + b² = c² where c is the hypotenuse (longest side, opposite the right angle). Example: 3² + 4² = 5² (the 3-4-5 right triangle).
Sets of whole numbers satisfying a²+b²=c²: 3-4-5, 6-8-10, 5-12-13, 8-15-17, 7-24-25. Multiples of these also work (e.g., 9-12-15).
SSS (all three sides equal), SAS (two sides + included angle), ASA (two angles + included side), AAS (two angles + non-included side), RHS (right angle + hypotenuse + side).
AA (two angles equal — most common), SSS (all sides in proportion), SAS (two sides in proportion + included angle equal). Similar triangles have equal angles and proportional sides.
(n−2) × 180° where n = number of sides. Triangle = 180°. Quadrilateral = 360°. Pentagon = 540°. Hexagon = 720°.
360° ÷ n where n = number of sides. The sum of all exterior angles of any convex polygon = 360°. Example: Regular hexagon exterior angle = 60°.
A = ½ × base × height. Also: A = ½ab sin C (using two sides and included angle). Also: Heron's formula A = √(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2.
A = πr² where r is the radius. Circumference = C = 2πr = πd where d is the diameter. π ≈ 3.14159.
A = ½ × (a + b) × h where a and b are the parallel sides (bases) and h is the perpendicular height between them.
V = πr²h where r = radius of base, h = height. Surface area = 2πr² + 2πrh (two circles + curved surface).
V = ⅓πr²h. Slant height l = √(r²+h²). Surface area = πr² + πrl (base + curved surface).
V = (4/3)πr³. Surface area = 4πr².
V = ⅓ × base area × height. For a square pyramid: V = ⅓ × s² × h.
1. Angle at centre = 2 × angle at circumference (same arc). 2. Angles in same segment are equal. 3. Angle in semicircle = 90°. 4. Opposite angles in cyclic quadrilateral add to 180°. 5. Tangent is perpendicular to radius at point of contact.
Arc length = (θ/360°) × 2πr for angle θ in degrees. In radians: Arc length = rθ. A full circle arc (θ=360°) = full circumference = 2πr.
Sector area = (θ/360°) × πr² for angle θ in degrees. In radians: Sector area = ½r²θ.
(x−h)² + (y−k)² = r² where (h,k) is the centre and r is the radius. Standard form centred at origin: x² + y² = r².
The segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length.
The point where all three medians intersect. It is located ⅔ of the way from each vertex to the opposite midpoint. Also the triangle's centre of mass.
30-60-90: Sides in ratio 1 : √3 : 2. The side opposite 30° is shortest, opposite 60° is √3 times the shortest. 45-45-90: Sides in ratio 1 : 1 : √2.
Cube: SA = 6s² (6 identical square faces). Rectangular prism (cuboid): SA = 2(lw + lh + wh) where l=length, w=width, h=height.
