# Dynamic Geometry 1474: Butterfly Theorem, Circle, Chords, Midpoints, Step-by-step Illustration

The dynamic geometry figure below shows a circle O with M midpoint of a chord AB. Chords CD and EF pass through M.
Chords CF and DE intersect AB at G and H, respectively. Prove that M is the midpoint of
GH.

## Static Diagram of Geometry Problem 1474

## Poster of the Butterfly Theorem 1474 using iPad Apps

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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.

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