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if KS=LS,NS=MS then <KSN=<MSL (Caucasus 2015 geometry for 8th grade)

Source: I Caucasus 2015 8.2

September 6, 2018
geometryequal anglesequal segmentsconvex quadrilateral

Problem Statement

In the convex quadrilateral ABCDABCD, point KK is the midpoint of ABAB, point LL is the midpoint of BCBC, point MM is the midpoint of CD, and point NN is the midpoint of DADA. Let SS be a point lying inside the quadrilateral ABCDABCD such that KS=LSKS = LS and NS=MSNS = MS .Prove that ∠KSN=∠MSL\angle KSN = \angle MSL.
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