**Statements** | Reasons |

1. $\displaystyle \overline{AC}$ ┴ $\displaystyle \overline{BD}$ | 1. Given |

2. ∠AEB and ∠CEB are right angles | 2. Given |

3. ΔAEB and ΔCEB are right Δs | 3. Definition of Right triangles |

4. $\displaystyle \overline{AB}$ ≅ $\displaystyle \overline{BC}$ | 4. Given |

5. $\displaystyle \overline{BE}$ ≅ $\displaystyle \overline{BE}$ | 5. Reflexive Property of Segment Congruence |

6. ΔABE ≅ ΔCBE | 6. Hypotenuse-Leg Congruence Theorem |

7. $\displaystyle \overline{AE}$ ≅ $\displaystyle \overline{CE}$ | 7. Corresponding parts of ≅ Δs are ≅ |

8. $\displaystyle \overline{AC}$ ┴ $\displaystyle \overline{DE}$ [I'm kinda confused by this, but $\displaystyle \overline{AC}$ ┴ $\displaystyle \overline{BD}$ has already been stated.] | 8. Definition of Perpendicular lines |

9. ΔAED and ΔCED are right Δs | 9. Definition of a Right Triangle |

10. $\displaystyle \overline{DE}$ ≅ $\displaystyle \overline{DE}$ | 10. Reflexive Property of Segment Congruence |

11. ΔAEB≅ ΔCEB | 11. Leg-Leg Congruence Theorem |

12. $\displaystyle \overline{AD}$ ≅ $\displaystyle \overline{CD}$ | 12. Corresponding parts of ≅ Δs are ≅ |