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For spreading the message 'save girl child save future' a rally was organized by some students of a school. they were given triangular cardboard piece.PQR

which they divided in to two parts by drawing the angle bisectors QO and RO of base angles Q and R and wrote a slogan . prove that angle QOR=90 degree+1/2angleP. what is the benefit of these types of rallies?



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Proof of  ∠QOR = 90° + ∠P/2

As PQR is a Δ,  
∠P + ∠Q + ∠R = 180°.
∠Q + ∠R = 180° - ∠P
∠Q + ∠R)/2 = 90° - ∠P/2        ---- (1)

∠OQR + ∠ORQ + ∠QOR = 180°
∠Q /2 + ∠ R/2  + ∠QOR = 180°
Substituting from (1):  90 -
∠P/2 + ∠QOR = 180°
∠QOR   = 90° + P/2  

   Writing mathematical and simple equations on placards is to attract the attention of the public in a new way.  Also it means to attract children and students towards the slogan "Save Girl Child, Save Future".
  Further, it also means that girls can do maths also.  The triangle is a symbol for the family.  Wide at one vertex, Husband at one vertex and the children at the third vertex.

   A girl or women is symbolized by the triangle. One part is herself.  The other part is the future of mankind. Because it is the girl who will give birth to future men and women.  So if girls are killed in the womb itself (foeticide) then future of the human race will be in trouble. 

See the diagram too.
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