Page 3 - EXERCISE 7.3

MAHEISHANG CLASS IX BOSEM
BOOKS AND TUTORIAL

Q5. Prove that in a quadrilateral, the sum of all the sides is greater than the sum of its diagonals.

soln:

we know , sum of two sides of a triangle is greater than the third side
to prove :- AB+BC+CD+DA>AC+BD
proof:
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In ABC
AB BC  AC  eqn 1
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In ADC
DA+CD>AC  eqn 2
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In BAD
AB+DA>BD  eqn 3
In BCD
BC+CD>BD  eqn 4
adding eqn 1,eqn 2,eqn 3 and eqn 4,we get

AB+BC+DA+CD+AB+DA+BC+CD>AC+AC+BD+BD
 2AB  2BC  2CD  2DA  2AC  2BD
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
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  2 AB BC CD DA    
 2 AC BD
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 AB BC CD DA  AC BD h/p
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
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Q6.In PQR , S is any point on the side QR .Show that PQ QR PR  2PS .


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soln:

given : In PQR ,S is on side QR

to prove:- PQ QR PR  2PS

proof :

In PQS
PQ+QS>PS  eqn 1
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In PRS
SR+PR>PS  eqn 2
adding eqn 1 and eqn 2,we get
PQ+QS+SR+PR  PS  PS


 PQ QR PR  2PS QS+SR QR 
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