Diagonals ac and bd form right angles at point m in parallelogram abcd. Prove abcd is a rhombus. 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
