≅∥∠Δ∽⊥
Given: rhombus ABCD, E is the midpoint of DF
PROVE: AD is congruent to BF
1. AD∥BC Opposite sides of parallelogram ABCD are ≅
2. ∠A≅∠EBF Corresponding angles, ∥ lines AD,BC cut by transversal AF.
3. ∠A≅∠C Opposite angles of parallelogram ABCD are ≅
4. ∠C≅∠EBF Angles ≅ same angle are ≅ to each other, 2,3
5. EF≅ED Given that E is the midpoint of DF
6. AB∥CD Opposite sides of parallelogram ABCD are ≅
7. AF∥CD AF is an extension of AB, 6
8. ∠BFE≅∠CDE Alternate interior angles,∥ lines AF,CD cut by transversal DF.
9. ΔEBF≅ΔECD AAS, 4,8,5
10. BF≅CD CPCT, 9
11. CD≅AD All sides of rhombus ABCD are ≅
12. AD≅BF Things ≅ same thing are ≅ to each other, 10,11
Edwin
