3
Problems(2)
isosceles trapezoid criterion, sum of lengths of sides and diagonals related
Source: 2007 Oral Moscow Geometry Olympiad grades 10-11 p3
10/19/2020
In a trapezoid, the sum of the lengths of the side and the diagonal is equal to the sum of the lengths of the other side and the other diagonal. Prove that the trapezoid is isosceles.
geometrytrapezoidisosceles
paralellogram construction, 3 midpoints given, 2 of altitudes, 1 of side
Source: 2007 Oral Moscow Geometry Olympiad grades 8-9 p3
10/18/2020
Construct a parallelogram , if three points are marked on the plane: the midpoints of its altitudes and and the midpoint of the side .
geometryparallelogramconstructionmidpoints