Given: lpqn is a rectangle, pm = qm

prove: lm = mn

The Proof is given below.

Step-by-step explanation:

Given:

LPQN is a Rectangle

PM = QM

To Prove:

LM = MN

Proof:

In  ΔLPM  and Δ NQM

LP ≅ NQ              ……{ Opposite sides of a Rectangle are congruent }  

∠L ≅ ∠N =90°     ……{ Measure of each vertex angle of rectangle are 90° }

PM ≅ QM            ……{ Given }  

ΔLPM ≅ ΔNQM  …{ By Hypotenuse Leg congruence test }

∴ LM ≅ MN    {corresponding parts of congruent triangle }Proved

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step-by-step explanation:

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