I'm given a rhombus (BCDE) and I am supposed to make a proof. There is a diagonal across the rhombus from C to E. I am given that CE bisects angle BCD and BED. I am supposed to prove that BE is congruent to DE.
If you could help me at least start writing the proof in list form, with statements and reasons, that'd be much appreciated! Thanks! :D
Sure! I'd be happy to help you write the proof. Here's a step-by-step list of statements and reasons for the proof:
1. Given: Rhombus BCDE with diagonal CE.
2. Given: CE bisects angle BCD and BED.
3. Definition of rhombus: All sides of a rhombus are congruent.
4. Definition of bisect: A line that divides an angle into two congruent angles.
5. Therefore, angles BCD and BED are congruent.
(Reason: Given that CE bisects angles BCD and BED)
6. Diagonal CE of a rhombus bisects each other into two congruent segments.
(Reason: Property of diagonals in a rhombus)
7. Therefore, segment BE is congruent to segment DE.
(Reason: Diagonal CE bisects segment BE and segment DE)
And there you have it! This list provides a logical progression of statements and reasons to prove that BE is congruent to DE in the given rhombus with the diagonal CE. I hope this helps you get started with your proof!