Question

Given:
MNOP is a parallelogram
Prove:
PM  ON
(For this proof, use only the definition of a parallelogram; don’t use any properties)

Answer 1

Answer:

$\overline{PM}\cong\overline{ON}$:, Segment subtended by the same angle on two adjacent parallel lines are congruent

Step-by-step explanation:

Statement,                                              Reason

MNOP is a parallelogram:,                     Given

$\overline{PM}\left | \right |\overline{ON}$:,                                               Opposite sides of a parallelogram

∠PMO ≅ ∠MON:,                                    Alternate Int. ∠s Thm.

$\overline{MN}\left | \right |\overline{PO}$:,                                               Opposite sides of a parallelogram

∠POM ≅ ∠NMO:,                                    Alternate Int. ∠s Thm.

OM ≅ OM:,                                               Reflexive property

$\overline{PM}\cong\overline{ON}$:,                                               Segment subtended by the same                                                                                                                              angle and on two adjacent parallel lines are congruent