Given: ABCE is a rectangle. D is the midpoint of Line CE
Prove: Line AD ≅ Line BD
Statements:
1) ABCE is a rectangle. D is the midpoint of Line Ce
2) ∠ AED ≅ ∠ BCD
3) Line AE ≅ Line BC
4) ?
5)?
6)?
Reasons
1)Given
2) Definition of rectangle
3) Definition of rectangle
4)?
5)?
6)?
4) AD and BD are opposite sides of a rectangle, so they are congruent. This follows from the properties of a rectangle, where opposite sides are congruent.
5) Line AD and line BD are congruent, and they share the same endpoint at point D. Therefore, AD ≅ BD by the reflexive property of congruence.
6) Alternatively, we can use the midpoint theorem to prove that AD ≅ BD. Since D is the midpoint of CE, AD and BD are both bisected by the same point, D. This implies that AD ≅ BD.