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