ABCDE is a Pentagon .prove that
Answers
Answered by
4
ApplyingtrinagleruleofvectoradditioninthetriangleABC,weget
AC
=
AB
+
BC
−−−(1)
Similarly,intriangleADEandtriangleACDweget
DA
=
DE
+
EA
−−−−(2)
AC
=
CD
+
AD
−−−−(3)
Therefore,
AB
+
BC
+
CD
+
DE
+
EA
Letusgrouptheaboveexpression,
(
AB
+
BC
)+
CD
+(
DE
+
EA
)
=
AC
+
CD
+
DA
Substitutingequation(1)
=
AD
+
DA
=
AD
−
AD
=0
Hence,proved.
Attachments:
Similar questions