MathDB

2

Part of 2012 Oral Moscow Geometry Olympiad

Problems(2)

equal polygons with vertices of one interior or on border of other, coincide?

Source: 2012 Oral Moscow Geometry Olympiad grades 8-9 p2

9/8/2019
Two equal polygons FF and F′F' are given on the plane. It is known that the vertices of the polygon FF belong to F′F' (may lie inside it or on the border). Is it true that all the vertices of these polygons coincide?
congruentpolygoninteriorgeometry
<A = <C = 90^o, AB = AE, BC = CD, AC = 1, area of convex ABCD

Source: 2012 Oral Moscow Geometry Olympiad grades 10-11 p2

9/25/2019
In the convex pentagon ABCDEABCDE: ∠A=∠C=90o\angle A = \angle C = 90^o, AB=AE,BC=CD,AC=1AB = AE, BC = CD, AC = 1. Find the area of the pentagon.
geometryareapentagon