# Geometry Problem 1565: Find the Length of BF in Triangle ABC Involving Median, Perpendicular, Midpoint, and Congruence.

In triangle ABC, BD is a median, and AE is
perpendicular to BD. Point F is on segment BE such that CF is congruent to AB. If DE = 5, find the length of BF.

Median cuts in two,

Perpendicular splits a side more.

BF length remains veiled.

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Academic Levels: Suitable for High School and College Mathematics
Education

## Key Definitions and Descriptions

Vocabulary |
Description |

Triangle ABC |
A triangle with vertices at points A, B, and C. |

Median BD |
A line segment from vertex B to the midpoint of the opposite side AC. |

Perpendicular AE |
A line segment from point A perpendicular to BD, intersecting BD at point E. |

Point F |
A point on segment BE such that CF is congruent (equal in length) to AB. |

DE |
The length of segment DE, which is given as 5 units. |

BF |
The length of segment BF, which is to be found. |

Congruent |
Having the same size and shape. In this context, CF is congruent to AB. |

##
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