ABCD is a rectangle are the midpoints of the sides ab BC CD and respectively if KN = 3 cm ab = 5 cm then find BD and LM what kind of quadrilateral is k l m n justify your answer
Answers
kn=3cm
ab=5cm
5*3=15cm
Given : ABCD is rectangle .
K L M N are the mid points of AB , BC , CD & DA respectively
KN = 3
To Find : BD and LM
what kind of quadrilateral is k l m n justify your answer
Solution:
in ΔABD
K & N are mid points of AB & AD
line joining the mid-point of two sides of a triangle is equal to half the length of the third side and parallel to third side
=> KN = BD/2
=> 3 = BD/2
=> BD = 6 cm
also KN || BD
similarly LM = = BD/2 = 3 cm
LM = 3 cm
LM || BD
Hence KN || BD
KN² = AK² + AN² = (AB/2)² + (AD/2)² = (AB² + AD² )/4
KL² = BK² + BL² = (AB/2)² + (BC/2)² = (AB² + BC² )/4
BC = AD
hence KN² = KL²
=> KN = KL
KN = KL = LM = MN
Hence KLMN is a rhombus
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