Can you crack it
Consider a
Convex quadrilateral ABCD
_ such that
K,L,M,N
are the MIDPOINTS of AB,BC,CA,AD respectively.Now suppose
(a)
BD bisects KM at Q
(b)
QA=QB=QC=QD
and
(c)
=
Then the quadrilateral is a.......
NOTE :
-merely guessing the answer won't improve your math skills.Try to prove it.
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1 solution
2nd statement gives ABCD is cyclic.Using angles on the same segment ,we get ABCD is a rectangle.Putting some basic class 9 geometry(midpoint theorem, properties of quadrilaterals bla bla bla),we find perpendicular from L to KL (say LP perpendicular to KL),from congruence of triangles LPK and LPM,we get LK=LM.So,BC=CD,and ABCD becomes a rectangle with adjacent sides equal;it is a square.