MathDB

2

Part of 1976 Bundeswettbewerb Mathematik

Problems(2)

Bundeswettbewerb Mathematik 1976 Problem 1.2

Source: Bundeswettbewerb Mathematik 1976 First round

9/11/2022
Each of the two opposite sides of a convex quadrilateral is divided into seven equal parts, and corresponding division points are connected by a segment, thus dividing the quadrilateral into seven smaller quadrilaterals. Prove that the area of at least one of the small quadrilaterals equals 1\slash 7 slash of the area of the large quadrilateral.
geometryareaquadratilateral
Bundeswettbewerb Mathematik 1976 Problem 2.2

Source: Bundeswettbewerb Mathematik 1976 Round 2

9/22/2022
Two congruent squares QQ and Q′Q' are given in the plane. Show that they can be divided into parts T1,T2,…,TnT_1, T_2, \ldots , T_n and T1′,T2′,…,Tn′T'_1 , T'_2 , \ldots , T'_n, respectively, such that Ti′T'_i is the image of TiT_i under a translation for i=1,2,…,n.i=1,2, \ldots, n.
geometrygeometric transformationsquareequal areasTranslation