# OK Geometry Report

Author:: | -
Source: | C:\Users\Zlatan\zm\Proj\GeoOkApp\Examples\OkEditEx_1.pro
Comment: |

## TASK

| 1 In an arbitrary quadrilateral mark the midpoints of the four sides. Which interesting properties of the obtained configuration can you spot?

## WORKOUT

2 same ratio BE:AB=BF:BC [=1:2] | 3 similar triangles ABC,BEF | 4 parallel lines EF|HG,EH|FG
5 parallelogram EFGHE |  |

## Notes

2 True by construction since E,F,G,H are the midpoints of the four sides.

3 The two triangles ave a common angle B. The ratio of the respective sides is BF:BC and BE:BA is the same, namely 1:2. Thus the two triangles are similar.

4 From #3 it follows that EF is parallel to AC. By analogy GH is also parallel to AC. Therefore EF and GH are parallel. In the same way we conclude that EH is parallel to FG. Therefore EFGH is a parallelogram.

5 According to #4, EFGH is a parallelogram,

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