Master Triangles & Polygons: 136 Geometry Flashcards from Centroids to Pick's Theorem

Triangles are the atoms of geometry: every polygon can be cut into them. The Triangles & Polygons deck (code VK7408, 136 cards) on Flip It walks that exact path — from the three types of triangle to the four triangle centers, then quadrilaterals, then general polygons. This guide shows what is inside and how to memorize it without mixing up your orthocenters and circumcenters.

Sample cards from the deck

What the 136 cards cover

• Triangle basics (cards 1–17): equilateral, isosceles, scalene, right, acute, obtuse; base, apex, altitude; area = ½ × base × height; perimeter; triangle inequality.
• The four centers (18–40): perpendicular bisectors → circumcenter and circumcircle; altitudes → orthocenter (inside, at the right-angle vertex, or outside); angle bisectors → incenter, incircle, inradius; medians → centroid and the 2:1 ratio; nine-point circle and Euler's line.
• Theorems and criteria (41–62): Thales' theorem, exterior angle theorem, AA / SAS / SSS similarity, SAS / ASA / SSS / AAS congruence, Pythagorean theorem and triples (3-4-5, 5-12-13), Heron's formula, law of sines, law of cosines, sine / cosine / tangent ratios, A = ½ab·sin(C).
• Applications (63–75): rigidity of triangles, trusses and roof gables, triangulation in surveying, tetrahedra, degenerate triangles.
• Quadrilaterals (76–103): trapezoid, isosceles trapezoid, parallelogram, rhombus, rectangle, square, kite, tangential, cyclic and bicentric quadrilaterals, orthodiagonal and equidiagonal, concave and self-intersecting; diagonal area formula, Bretschneider's and Brahmagupta's formulas, bimedians, Varignon parallelogram, Euler's quadrilateral theorem.
• General polygons (104–136): simple, convex, concave, regular, equilateral, equiangular; interior and exterior angle sums; shoelace formula, Pick's theorem, isoperimetric inequality, apothem area formula; star, cyclic, tangential, spherical, skew and rectilinear polygons; pentagon through dodecagon, apeirogon.

Two memory tricks that actually work here

Tie each center to its construction line, not to its name. The deck asks the same question four times — "where do the three X meet?" — and the answers are easy to swap. Build one mental image: perpendicular bisectors find the point equidistant from the vertices (circumcenter, so a circle around); angle bisectors find the point equidistant from the sides (incenter, so a circle inside); medians balance mass (centroid); altitudes have no circle at all (orthocenter). When a card comes up, say the construction line out loud before the answer.

Learn the quadrilateral family as a set of inheritances. Cards 101–103 list which shapes have bisecting, perpendicular or equal diagonals. Instead of memorizing three lists, remember that a square inherits everything from both rhombus (perpendicular diagonals) and rectangle (equal diagonals), and all three are parallelograms (bisecting diagonals). The lists then reconstruct themselves.

Order of study

Triangles (cards 1–62) to 90 % recall first, then quadrilaterals, then polygons. Give the formula cards — Heron, law of cosines, shoelace, Pick — one pass with pen and paper, one worked example each.

Sign in to Flip It, search for VK7408 or "Triangles & Polygons" in the library, and start with the triangle basics.