Left Panel Interactive

Statements

Reasons

1. ABCD is a parallelogram

1. given

2. AC bisects ∠BCD and ∠BAD

2. given

3. BD bisects ∠CDA and ∠ABC

3. given

4. ∠ABE ≅ ∠CBE;
∠ADE ≅ ∠CDE

4. def. of bisects

5. ∠ABE and ∠CDE are alt. int. ∠s

5. def. of alternate interior angles

6. ∠ADE and ∠CBE are alt. int. ∠s

6. def. of alternate interior angles

7. ∠ABE ≅ ∠CDE;
∠ADE ≅ ∠CBE;

7. alternate interior angles are congruent

8. ∠ABE ≅ ∠ADE ≅ ∠CDE ≅ ∠CBE

8. transitive property

9. ∠BAE ≅ ∠BCE ≅ ∠DCE ≅ ∠DAE

9. similar argument as steps 4 - 8

10. BE ≅ DE

10. diagonals of a parallelogram bisect each other

11.△ABE ≅ △CBE ≅ △CDE ≅ △ADE

11. AAS

12. AB ≅ CB ≅ CD ≅ AD

12. CPCTC

13. ABCD is a rhombus

13. def. of rhombus