# Geometry Problem 1459: Two Triangles, Orthocenter, Midpoint, Perpendicular

The figure shows the vertical angles BAC and DAE. F and G are the orthocenters of trianglers ABC and ADE, respectively. If M and N are the midpoints of BE and CD, respectively, prove that MN and FG are perpendicular.

## Poster of the problem 1459 using iPad Apps

### Classroom Resource:Interactive step-by-step animation using GeoGebra

This step-by-step interactive illustration was created with GeoGebra.

• To explore (show / hide): click/tap a check box.
• To stop/play the animation: click/tap the icon in the lower left corner.
• To go to first step: click/tap the "Go to step 1" button.
• To manipulate the interactive figure: click/tap and drag the blue points or figures.

GeoGebra is free and multi-platform dynamic mathematics software for all levels of education that joins geometry, algebra, tables, graphing, statistics and calculus application, intended for teachers and students. Many parts of GeoGebra have been ported to HTML5.