In the figure HE is the median of triangle HOT . M is the midpoint of HE . OM meets HT at N. prove that HN=1/3HT
In the figure HE is the median of triangle HOT . M is the midpoint of HE . OM meets HT at N. prove that HN=1/3HT
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Proved that HN = HT/3 , if HE is the median of triangle HOT , M is midpoint of HE & OM meets HT at N
Step-by-step explanation:
Draw a line EP ║ ON ║ MN ( M is point on ON)
in Δ HMN & ΔHEP
MN ║ EP
=> HM / ME = HN /NP
HM = ME M is mid point of HE
=> HN /NP = 1
=> HN = NP
Now in ΔTEP & ΔTON
EP ║ ON
=> TE/EO = TP/NP
TE = EO ( as HE is miedian )
=> TP/NP = 1
=> TP = NP
HN = NP = TP
HT = HN + NP + TP
=> HT = HN + HN + HN
=> HT = 3HN
=> HN = HT/3
QED
Proved
Learn More :
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