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Properties of Angles Formed by Two Parallel Lines and a Transversal

Diagonals LS ...

Question

Diagonals LS and BN of rectangle BSNL intersect each other at point K. If KL =7cm, find LS and BN (see fig)

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Solution

$I n p a r a l l e l o g r a m B S N L, B S = L N & B S ∥ L N . I f B S ∥ L N & B N i s t h e t r a n s v e r s a l t h e n ∠ L N K = ∠ S B K {A l t e r n a t e a n g l e s} I f B S ∥ L N & S L i s t h e t r a n s v e r s a l t h e n ∠ K L N = ∠ K S B {A l t e r n a t e a n g l e s} I n △ L K N & △ S K B, ∠ L N K = ∠ S B K B S = L N ∠ K L N = ∠ K S B S o △ L K N ≅ △ S K B {B y A S A R u l e o f C o n g r u e n c y} S o K L = S K G i v e n K L = 7 c m \Rightarrow L S = 2 K L = 2 \times 7 = 14 c m I n a r e c t a n g l e b o t h d i a g o n a l s a r e e q u a l, s o B N = L S = 14 c m$

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