Question

Plzz answer this questions fast...
ques.no. 3, 6 and 8.

plzzz do fast...

Answer 1

que 3
ans. Given: D,E,F are the mid points of AB,BC,CA
To Prove: DE = EF
Proof: AB = AC (isosceles triangle) 
          ∠B = ∠C (angle opp to equal sides)
          ¹/₂ AB = ¹/₂ AC
          so,DB = CF
          In ΔADF and ΔCEF
              DB = CF (proved above)
              BE = CE (E is the mid point of BC)
             ∠B = ∠C (proved above)
          ∴ ΔADF = ΔCEF (SAS)
               DE = FE (CPCT)
Hence, Proved
que 6
ans. Let a square ABCD in which L,M,N&O are the midpoints .

in triangle AML and triangle CNO 
       AM = CN ( AB = DC and M and O are the midpoints )
       AL = CM ( AD = BC and L and   N are the midpoints )
       angle MAL = angle NCO ( all angles of a square = 90 degree )
      by AAS critaria
        triangle AML CONGRUENT to triangle CNO
    therefore ML = ON  ( CPCT  )
similarly in triangle MBN CONGRUENT to  LDO  and 
    AND triangle  AML is CONGRUENT  to triangle
now , 
  in Triangle AML ,
 angle AML = angle ALM ( AM = AL ) 
                   = 45 degree
   similarly in triangle LDO 
   angle DLO = 45 degree
 there fore ,
 angle MLO = 90 degree 

by the properties of SQUARE 
 all sides are equal and angles are 90 degree

hope you understand