Triangle angle sum theorem: The three angles of a triangle add up to 180°
Exterior angle theorem: An exterior angle of a triangle equals the sum of the two remote interior angles
Isosceles triangle theorem: Angles opposite equal sides are equal
Converse of the isosceles triangle theorem: Sides opposite equal angles are equal
Triangle inequality theorem: The sum of any two sides is greater than the third side
Pythagorean theorem: In a right triangle, a² + b² = c²
Converse of the Pythagorean theorem: If a² + b² = c², the triangle is a right triangle
45-45-90 triangle: Sides are in the ratio 1 : 1 : √2
30-60-90 triangle: Sides are in the ratio 1 : √3 : 2
Midsegment theorem: A segment joining midpoints of two sides is parallel to the third side and half as long
Triangle angle bisector theorem: An angle bisector splits the opposite side in the ratio of the adjacent sides
SSS congruence: Three pairs of equal sides make triangles congruent
SAS congruence: Two sides and the angle between them equal makes triangles congruent
ASA congruence: Two angles and the side between them equal makes triangles congruent
AAS congruence: Two angles and a non-included side equal makes triangles congruent
HL congruence: Right triangles with equal hypotenuse and one equal leg are congruent
CPCTC: Corresponding parts of congruent triangles are congruent
AA similarity: Two triangles with two equal angles are similar
SAS similarity: Two proportional sides with equal included angle make triangles similar
SSS similarity: Three proportional sides make triangles similar
Vertical angles theorem: Vertical angles are equal
Linear pair postulate: Two angles that form a straight line add up to 180°
Corresponding angles postulate: Parallel lines cut by a transversal make equal corresponding angles
Alternate interior angles theorem: Parallel lines cut by a transversal make equal alternate interior angles
Same-side interior angles theorem: Parallel lines cut by a transversal make supplementary same-side interior angles
Perpendicular bisector theorem: A point on the perpendicular bisector is equally far from the segment's endpoints
Angle bisector theorem (points): A point on an angle bisector is equally far from the angle's sides
Centroid: The point where a triangle's three medians meet
Circumcenter: The point where perpendicular bisectors meet; the center of the circumscribed circle
Incenter: The point where angle bisectors meet; the center of the inscribed circle
Orthocenter: The point where a triangle's altitudes meet
Centroid ratio: The centroid divides each median in a 2 : 1 ratio, longer part toward the vertex
Inscribed angle theorem: An inscribed angle is half its intercepted arc
Central angle theorem: A central angle equals its intercepted arc
Thales' theorem: An angle inscribed in a semicircle is a right angle
Tangent-radius theorem: A tangent is perpendicular to the radius at the point of tangency
Two tangents theorem: Tangent segments from one outside point to a circle are equal
Chord-chord theorem: If two chords cross, the products of their pieces are equal
Opposite angles in a cyclic quadrilateral: They add up to 180°
Parallelogram theorem: sides: Opposite sides are equal
Parallelogram theorem: angles: Opposite angles are equal; consecutive angles add up to 180°
Parallelogram theorem: diagonals: Diagonals bisect each other
Rectangle diagonals: Diagonals of a rectangle are equal
Rhombus diagonals: Diagonals are perpendicular and bisect the angles
Kite diagonals: Diagonals are perpendicular
Isosceles trapezoid base angles: Base angles of an isosceles trapezoid are equal
Side-splitter theorem: A line parallel to one side of a triangle divides the other two sides proportionally
Geometric mean (altitude) theorem: The altitude to the hypotenuse of a right triangle is the geometric mean of the two segments it makes
Law of sines: a/sin A = b/sin B = c/sin C
Law of cosines: c² = a² + b² − 2ab cos C
Euler line: The centroid, circumcenter and orthocenter of a triangle lie on one line
Ceva's theorem: Cevians through a point in a triangle satisfy (AF/FB)(BD/DC)(CE/EA) = 1
Pick's theorem: Area of a lattice polygon = i + b/2 − 1, with i inside points and b boundary points
Euler's polyhedron formula: V − E + F = 2

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