In figure 5.53 $□$ PQRS and $□$ MNRL are rectangles.
Where M is the mid-point of PR. Prove that i) SL = LR ii) LN = $\frac{1}{2}$ SQ

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Solution

$Given : □ PQRS and □ MNRL are rectangles . M is the midpoint of PR Construction : Join S and Q, L and N To prove : (i) SL = LR Since, RQ ∥ SP (□ PQRS is a rectangle) and RN ∥ LM (□ MNRL is a rectangle) Hence, SP ∥ LM Now, In ∆ PRS Since, M is the mid point of PR and SP ∥ LM Hence, by converse of mid point theorem L is the midpoint of RS or, SL = LR Similarly, N is the midpoint of RQ . (ii) L and N are the midpoints of RS and RQ, respectively . Now, consider △ SRQ . Here, LN = \frac{1}{2} SQ (By the midpoint theorem)$

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