Statements
Reasons
1. ABCD is a parallelogram
1. given
2. ZAMB, BMC, 2CMD, and ZDMA are right angles 2. given
3. ZAMB – BMC – 2 CMD = ZDMA
3. right angles are congruent
4. AC bisects BD;
4. diagonals of a parallelogram bisect each other
BD bisects AC;
5.AM MC, MB MD
5. definition of a bisector
16.12
6. SAS congruency theorem
7. AB BC - CD - DA
7. CPCTC
8. figure ABCD is a rhombus
8. definition of a rhombus
ABC = ADC ~ ABAD > ABCD
AMB > ACMB - ACMD > AMD
Ο ΔΑΒC 2 ΔΑDC 2 ΔAMD ε ΔBMC
Ο ΔΑΜΒ α ΔCMD ΔBAD α ΔBCD