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 parallelogram1.given 2.∠AMB, ∠BMC, ∠CMD, and ∠DMA are right angles2.given 3.∠AMB ≅ ∠BMC ≅ ∠CMD ≅ ∠DMA3.right angles are congruent 4.AC bisects BD; BD bisects AC;4.diagonals of a parallelogram bisect each other 5.AM ≅ MC, MB ≅ MD5.definition of a bisector 6.?6.SAS congruency theorem 7.AB ≅ BC ≅ CD ≅ DA7.CPCTC 8.figure ABCD is a rhombus8.definition of a rhombus △ABC ≅ △ADC ≅ △BAD ≅ △BCD △AMB ≅ △CMB ≅ △CMD ≅ △AMD △ABC ≅ △ADC ≅ △AMD ≅ △BMC △AMB ≅ △CMD ≅ △BAD ≅ △BCD