#separator:tab #html:false #tags column:4 Triangle angle sum theorem The three angles of a triangle add up to 180° math-geometry-theorems Exterior angle theorem An exterior angle of a triangle equals the sum of the two remote interior angles math-geometry-theorems Isosceles triangle theorem Angles opposite equal sides are equal math-geometry-theorems Converse of the isosceles triangle theorem Sides opposite equal angles are equal math-geometry-theorems Triangle inequality theorem The sum of any two sides is greater than the third side math-geometry-theorems Pythagorean theorem In a right triangle, a² + b² = c² math-geometry-theorems Converse of the Pythagorean theorem If a² + b² = c², the triangle is a right triangle math-geometry-theorems 45-45-90 triangle Sides are in the ratio 1 : 1 : √2 math-geometry-theorems 30-60-90 triangle Sides are in the ratio 1 : √3 : 2 math-geometry-theorems Midsegment theorem A segment joining midpoints of two sides is parallel to the third side and half as long math-geometry-theorems Triangle angle bisector theorem An angle bisector splits the opposite side in the ratio of the adjacent sides math-geometry-theorems SSS congruence Three pairs of equal sides make triangles congruent math-geometry-theorems SAS congruence Two sides and the angle between them equal makes triangles congruent math-geometry-theorems ASA congruence Two angles and the side between them equal makes triangles congruent math-geometry-theorems AAS congruence Two angles and a non-included side equal makes triangles congruent math-geometry-theorems HL congruence Right triangles with equal hypotenuse and one equal leg are congruent math-geometry-theorems CPCTC Corresponding parts of congruent triangles are congruent math-geometry-theorems AA similarity Two triangles with two equal angles are similar math-geometry-theorems SAS similarity Two proportional sides with equal included angle make triangles similar math-geometry-theorems SSS similarity Three proportional sides make triangles similar math-geometry-theorems Vertical angles theorem Vertical angles are equal math-geometry-theorems Linear pair postulate Two angles that form a straight line add up to 180° math-geometry-theorems Corresponding angles postulate Parallel lines cut by a transversal make equal corresponding angles math-geometry-theorems Alternate interior angles theorem Parallel lines cut by a transversal make equal alternate interior angles math-geometry-theorems Same-side interior angles theorem Parallel lines cut by a transversal make supplementary same-side interior angles math-geometry-theorems Perpendicular bisector theorem A point on the perpendicular bisector is equally far from the segment's endpoints math-geometry-theorems Angle bisector theorem (points) A point on an angle bisector is equally far from the angle's sides math-geometry-theorems Centroid The point where a triangle's three medians meet math-geometry-theorems Circumcenter The point where perpendicular bisectors meet; the center of the circumscribed circle math-geometry-theorems Incenter The point where angle bisectors meet; the center of the inscribed circle math-geometry-theorems Orthocenter The point where a triangle's altitudes meet math-geometry-theorems Centroid ratio The centroid divides each median in a 2 : 1 ratio, longer part toward the vertex math-geometry-theorems Inscribed angle theorem An inscribed angle is half its intercepted arc math-geometry-theorems Central angle theorem A central angle equals its intercepted arc math-geometry-theorems Thales' theorem An angle inscribed in a semicircle is a right angle math-geometry-theorems Tangent-radius theorem A tangent is perpendicular to the radius at the point of tangency math-geometry-theorems Two tangents theorem Tangent segments from one outside point to a circle are equal math-geometry-theorems Chord-chord theorem If two chords cross, the products of their pieces are equal math-geometry-theorems Opposite angles in a cyclic quadrilateral They add up to 180° math-geometry-theorems Parallelogram theorem: sides Opposite sides are equal math-geometry-theorems Parallelogram theorem: angles Opposite angles are equal; consecutive angles add up to 180° math-geometry-theorems Parallelogram theorem: diagonals Diagonals bisect each other math-geometry-theorems Rectangle diagonals Diagonals of a rectangle are equal math-geometry-theorems Rhombus diagonals Diagonals are perpendicular and bisect the angles math-geometry-theorems Kite diagonals Diagonals are perpendicular math-geometry-theorems Isosceles trapezoid base angles Base angles of an isosceles trapezoid are equal math-geometry-theorems Side-splitter theorem A line parallel to one side of a triangle divides the other two sides proportionally math-geometry-theorems Geometric mean (altitude) theorem The altitude to the hypotenuse of a right triangle is the geometric mean of the two segments it makes math-geometry-theorems Law of sines a/sin A = b/sin B = c/sin C math-geometry-theorems Law of cosines c² = a² + b² − 2ab cos C math-geometry-theorems Euler line The centroid, circumcenter and orthocenter of a triangle lie on one line math-geometry-theorems Ceva's theorem Cevians through a point in a triangle satisfy (AF/FB)(BD/DC)(CE/EA) = 1 math-geometry-theorems Pick's theorem Area of a lattice polygon = i + b/2 − 1, with i inside points and b boundary points math-geometry-theorems Euler's polyhedron formula V − E + F = 2 math-geometry-theorems