3. Reasons
Statements
MNOP is a parallelogram
N
PM || ON
M
Given:
Alternate Int. Zs Thm,
MNOP is a parallelogram
MN II PO
Alternate Int. Zs Thm,
Prove:
PM = ON
(For this proof, use only the
definition of a parallelogram;
don't use any properties)
HE

3. Distances between two parallel lines

4. = : Reason; Corresponding part of ΔACB and ΔDCE

C is the midpoint of : Reason;   = : Definition of midpoint

Step-by-step explanation:

3. A parallelogram is defined as a quadrilateral with two opposite sides equal and parallel and having equal opposite interior angles

MNOP is a parallelogram: Reason; Given

: Reason; Opposite sides of a parallelogram

∠NOM ≅ ∠OMP: Reason Alternate interior angles

: Reason; Opposite sides of a parallelogram

∠NMO ≅ ∠MOP: Reason Alternate interior angles

Distances between two parallel lines

4. : Reason; Given

∠EAB ≅ ∠AED: Reason; Alternate int. ∠s Thm

∠ABC ≅ ∠EDB : Reason; Alternate int. ∠s Thm

C is the midpoint of  : Reason; Given

= : Reason; Definition of midpoint

Therefore, ΔACB ≅ ΔDCE: Reason Angle Angle Side (AAS) Theorem

= : Reason; Corresponding part of ΔACB and ΔDCE

C is the midpoint of : Reason; Definition of midpoint