Given: Parallelogram MNOP with diagonals MO and NP
Prove: MO and NP bisect each other
Statements
Parallelogram MNOP with diagonals MO and NP
Move statements into the table to complete the proof that shows the diagonals of a parallelogram bisect each other.
MR OR, PR NR
MO and NP bisect each other
MNOP
and
ZROP ZRMN
R
MN || OP
ZRPO ZRNM
O
Reasons
Given
Definition of parallelogram
Alternate Interior angles formed by parallel lines are congruent
Opposite sides of a parallelogram are congruent
ASA
Corresponding parts of congruent triangles are congruent
Definition of bisector
NO
PM
ZRPM ZRNO
PM || NO
ARPMARNO
ZRMP ZRON
A ROPA RMN