To prove that the diagonals of rectangle LMNO are congruent, we begin by noting that in rectangle LMNO, points L, M, N, and O are the vertices of the rectangle, with P being the intersection of diagonals LN and MO. By the definition of a rectangle, we know that opposite sides are equal and parallel: \( LM = NO \) and \( LN = MO \) (Reason: Definition of a rectangle). Since P is the midpoint of both diagonals in rectangle LMNO, we can conclude that \( LP = PN \) and \( MP = PO \) (Reason: Diagonals of a rectangle bisect each other). Therefore, we can apply the congruence of triangles: triangles LPM and NPO are congruent by the Side-Side-Side (SSS) postulate, as \( LP = PN \), \( MP = PO \), and in both triangles, \( PM \) is common (Reason: SSS Congruence Postulate). Since corresponding parts of congruent triangles are congruent, we have \( LM = NO \) and \( LN = MO \). Therefore, we conclude that the diagonals \( LN \) and \( MO \) are congruent (Reason: Corresponding parts of congruent triangles are congruent). Thus, diagonals \( LN \) and \( MO \) in rectangle LMNO are congruent.
Prove that the diagonals of rectangle LMNO are congruent. write a paragraph proof, but be sure to include a reason for each of your statements.
their is P in the middle where LN and MO intersect
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