Congruence (geometry) — AMC & AIME Practice Problems | LIVE by Po-Shen Loh

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Congruence (geometry) — AMC & AIME Problems

Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses congruence (geometry) — a geometry concept — each with a professionally curated solution, many with a video solution too, from LIVE by Po-Shen Loh. Browse all concepts or the full past-contest archive.

All of these problems are used with official legal permission of the Mathematical Association of America (MAA).

AMC 8

2001 AMC 8 Problem 23 · 2006 AMC 8 Problem 19 · 2009 AMC 8 Problem 20 · 2012 AMC 8 Problem 25

AMC 10

2002 AMC 10A Problem 8 · 2005 AMC 10A Problem 8 · 2006 AMC 10B Problem 15 · 2021 AMC 10B Fall Problem 15 · 2022 AMC 10B Problem 16

AMC 12

1999 AMC 12 Problem 2 · 2002 AMC 12A Problem 8 · 2005 AMC 12A Problem 7 · 2012 AMC 12B Problem 21

AIME

2007 AIME II Problem 3 · 2019 AIME II Problem 1

More geometry concepts

3D geometry altitude angle bisector angle bisector theorem angle chasing angle sum annulus arc area area decomposition area ratio Brahmagupta’s Formula centroid chord circle circle area circumcircle, circumcenter, and circumradius circumference cone coordinate geometry cube geometry cyclic quadrilateral cylinder diagonal distance formula ellipse equiangular polygon equilateral triangle Euler’s Polyhedron Formula Heron’s Formula homothety hyperbola incircle, incenter, and inradius inscribed angle isosceles triangle kite lattice point law of cosines law of sines mass points median (geometry)midpoint net (3D geometry)paper folding parabola parallel lines parallelogram perimeter perpendicular bisector Pick’s Theorem polyhedron power of a point power scaling of length, area, and volume Ptolemy’s Theorem pyramid Pythagorean Theorem Pythagorean Triple radical axis rectangle rectangular prism reflection (geometry)regular polygon rhombus right triangle sector shoelace formula similarity special right triangle sphere square (geometry)Stewart’s Theorem surface area tangent circles tangent line transformation trapezoid triangle area triangle inequality trigonometric identity trigonometry vector Viviani’s Theorem volume