Question

Complete the two-column proof.



Statement
Reason
L
M
N
P
LMNP is a parallelogram with diagonals
L
N
‾
LN
and
M
P
‾
MP

Given
L
M
‾
≅
P
N
‾
;

L
P
‾
≅
M
N
‾
LM
≅
PN
;
LP
≅
MN



Reflexive Property of Congruence


∠
L
M
N
≅
∠
N
P
L
∠LMN≅∠NPL

DRAG & DROP THE ANSWER
Opposite sides of a parallelogram are parallel

Opposite sides of a parallelogram are congruent

Side-Side-Side Congruence

△
L
M
N
≅
△
N
P
L
△LMN≅△NPL

L
N
‾
≅
P
M
‾
LN
≅
PM


Diagonals of a parallelogram are congruent

Side-Angle-Side Congruence

L
N
‾
≅
L
N
‾
LN
≅
LN


△
K
M
N
≅
△
L
M
N
△KMN≅△LMN

Corresponding Parts of Congruent Triangles are Congruent

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Answer 1

Here is the completed two-column proof based on your provided framework:

| Statement | Reason |
|---------------------------------------------------------|----------------------------------------------------------|
| LMNP is a parallelogram with diagonals LN and MP | Given |
| LM ≅ PN | Opposite sides of a parallelogram are congruent |
| LP ≅ MN | Opposite sides of a parallelogram are congruent |
| LN ≅ PM | Diagonals of a parallelogram are congruent |
| ∠LMN ≅ ∠NPL | Alternate interior angles are congruent (or) Opposite angles are congruent in a parallelogram |
| ∆LMN ≅ ∆NPL | Side-Angle-Side Congruence |
| Corresponding Parts of Congruent Triangles are Congruent| By definition of congruence (CPCTC) |

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