A geometry problem by Johnson Du

Geometry Level 1

ABCD is a rectangle. BEGF is flipped from the original DECF which point D is replaced B. AB=3 AE=4 find BF=?


The answer is 5.

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Johnson Du by Johnson Du , 19, China

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2 solutions

Johnson Du
Feb 28, 2015

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We should observe the following since vertex D is flipped to B,
- EF is the bisector of BED - Diagonal BD is flipped itself and perpendicular to EF { since EB=ED} - Point F is the symmetrical of E respect to diagonal BD so BF equal BE Since BE is the hypotenuse of straight triangle BAE, since sides are 3 and 4 units, BE=5 =BF

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