Geometry, Plane Geometry, Plane Transformations, Congruence Transformations (Isometries), Parallel Translation / Translation

A translation is an isometry that shifts every point of a figure by the same distance in a given direction, often described by a vector. Questions involve finding the image of a point or figure after a translation or determining the translation vector.

• Question

  Given `12` intersecting lines in the plane. Prove that there exist two of these lines such that the angle between them is less than `17^@`.

  Show hint

  Log in here to receive the hint
  Topics:

  Combinatorics -> Pigeonhole Principle Geometry -> Plane Geometry -> Angle Calculation Geometry -> Plane Geometry -> Plane Transformations -> Congruence Transformations (Isometries) -> Parallel Translation / Translation

• Triangles on Lines

  Six congruent isosceles triangles are arranged as shown in the figure.
  Show that points C, F, and M are collinear.

  

  Show hint

  Log in here to receive the hint
  Topics:

  Geometry -> Plane Geometry -> Angle Calculation Geometry -> Plane Geometry -> Triangles -> Triangle Congruence Geometry -> Plane Geometry -> Plane Transformations -> Congruence Transformations (Isometries) -> Parallel Translation / Translation
  Sources:
  • Gillis Mathematical Olympiad, 2018-2019 Question 3