Maths Olympiad Prep

Track / Stage 4 / 17 of 340 #277 of 1964

Problem 277

AMC 12 late, AIME early
Geometry Difficulty 4.5 Find the answer

61. Can the plane be "tiled": a) with triangles equal to a given one; b) with quadrilaterals equal to a given one?

The source for this one didn't record the answer, so there is nothing to check what you type against. Work it on paper and mark yourself against the solution below.

Official solution

61. It is not difficult to prove that the diagonals of this quadrilateral serve as the bisectors of its angles, and such a convex quadrilateral is a rhombus.

62. a) possible, c) possible.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.