Diagonals AC and BD form right angles at point M in parallelogram ABCD. Prove ABCD is a rhombus. Parallelogram A B C D is shown. Diagonals are drawn from point A to point C and from point B to point D and intersect at point M. Sides A B and D C are parallel and sides B C and A D are parallel. A square is drawn around point M. Statements Reasons 1. ABCD is a parallelogram 1. given 2. ∠AMB, ∠BMC, ∠CMD, and ∠DMA are right angles 2. given 3. ∠AMB ≅ ∠BMC ≅ ∠CMD ≅ ∠DMA 3. right angles are congruent 4. AC bisects BD; BD bisects AC; 4. diagonals of a parallelogram bisect each other 5. AM ≅ MC, MB ≅ MD 5. definition of a bisector 6. ? 6. SAS congruency theorem 7. AB ≅ BC ≅ CD ≅ DA 7. CPCTC 8. figure ABCD is a rhombus 8. definition of a rhombus △ABC ≅ △ADC ≅ △BAD ≅ △BCD △AMB ≅ △CMB ≅ △CMD ≅ △AMD △ABC ≅ △ADC ≅ △AMD ≅ △BMC △AMB ≅ △CMD ≅ △BAD ≅ △BCD