If WZYX Is congruent to PMLN describes two quadrilaterals, which other statement is also true?

WXYZ Is congruent to LMNP
WXYZ Is congruent to NPML
WXYZ Is congruent to PNLM
WXYZ Is congruent to MLNP

1 answer

If the quadrilateral WZYX is congruent to the quadrilateral PMLN (denoted \( WZYX \cong PMLN \)), this means that their corresponding sides and angles are equal.

For congruent figures, the order of the vertices matters when determining the correspondence between their parts. To find a true statement about the congruence of these quadrilaterals, we need to identify the correct pairings of the vertices.

The congruences can be expressed in terms of corresponding vertices. If we assume:

  • \( W \) corresponds to \( P \)
  • \( Z \) corresponds to \( M \)
  • \( Y \) corresponds to \( L \)
  • \( X \) corresponds to \( N \)

Thus, we can express this relationship as:

  • \( W \) to \( P \)
  • \( Z \) to \( M \)
  • \( Y \) to \( L \)
  • \( X \) to \( N \)

From that, we can derive that \( WXYZ \) corresponds to \( PMLN \).

The correct statement that directly follows from the above congruence is:

WXYZ Is congruent to LMNP

This matches the order of the vertices according to their corresponding points being congruent, confirming that the statement is true.

So the answer is: WXYZ Is congruent to LMNP.