Proof Table
| Number | Statement | Reason |
|---|---|---|
| 1 | PARL is a parallelogram | Given |
| 2 | The diagonals of PARL are congruent | Given |
| 3 | PR = AL | Diagonals are congruent |
| 4 | PA = RL | Opposite sides of a parallelogram are congruent |
| 5 | AR = LP | Opposite sides of a parallelogram are congruent |
| 6 | Triangle APL = Triangle RLP | SSS Property of Congruence |
| 7 | Angle APL = Angle RLP | CPCTC |
| 8 | Triangle PAR = Triangle LRA | SSS Property of Congruence |
| 9 | Angle PAR = Angle LRA | CPCTC |
| 10 | (Angle APL)+(Angle RLP) = 180 | Same Side Interior angles are supplementary |
| 11 | (Angle APL)+(Angle APL) = 180 | Substitution (lines 10 and 7) |
| 12 | 2*(Angle APL) = 180 | Combine like terms |
| 13 | Angle APL = 90 degrees | Division Property of Equality |
| 14 | 90 degrees = Angle RLP | Substitution (lines 7 and 13) |
| 15 | Angle RLP = 90 degrees | Symmetric Property of Equality |
| 16 | Angle ARL = Angle APL | Opposite angles of a parallelogram are congruent |
| 17 | Angle ARL = 90 degrees | Substitution (lines 16 and 13) |
| 18 | Angle PAR = Angle RLP | Opposite angles of a parallelogram are congruent |
| 19 | Angle PAR = 90 degrees | Substitution (lines 18 and 15) |
| 20 | PARL has 4 right angles | See lines 13,15,17,19 |
| 21 | PARL is a rectangle | Definition of Rectangle (see note) |
Note: A rectangle is simply a quadrilateral with 4 right angles (aka 90 degree angles).