Question

3.

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

Answer 1

`\overline{PM}\cong\overline{ON}`: Reason; Corresponding parts of congruent triangles ΔOMN and ΔOMP are congruent (CPCTC)

Explanation:

1) MNOP is a parallelogram: Reason; Given

2)
`\overline{PM}\left | \right |\overline{ON}`: Reason; Definition of a parallelogram

3) ∠MON ≅ ∠PMO: Reason; Alternate Int. ∠s Thm.

4)
`\overline{MN}\left | \right |\overline{PO}`: Reason; Definition of a parallelogram

5) ∠NMO ≅ ∠POM: Reason; Alternate Int. ∠s Thm.

6)
`\overline{OM}\cong\overline{OM}`: Reason; Reflexive property

7) ΔOMN ≅ ΔOMP: Reason; Angle Angle Side (AAS) congruency theorem

8)
`\overline{PM}\cong\overline{ON}`: Reason; Corresponding parts of congruent triangles are congruent (CPCTC).

Also we have;

9)
`\overline{PM}\cong\overline{ON}`: Reason; Segment opposite congruent angles are congruent