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PLEASE HELP THIS IS A TIMED QUESTION ON A QUIZ!!!

9. If H is the centroid of ABDF, DF = 50, CF = 42, and BH = 22, find each missing measure.
a) HE =
d) DE =
e) CH=
b) EF=
c) HF =
f) BE =

PLEASE HELP THIS IS A TIMED QUESTION ON A QUIZ 9 If H is the centroid of ABDF DF 50 CF 42 and BH 22 find each missing measure a HE d DE e CH b EF c HF f BE class=

Respuesta :

mhanifa

Answer:

  • a)  11, d) 25, e) 14, b) 25, c) 28, f) 33

Step-by-step explanation:

Given

  • ΔBDF, with H is the centroid of BDF, DF = 50, CF = 42, and BH = 22

To find

  • HE , DE , CH, EF,  HF, BE

Solution

As per definition of the centroid, the points C, E and G are midpoints of respective sides and the length of short and long distances from the centroid have ratio of 1/3 and 2/3 of median

  • a) HE =  1/2BH = 1/2(22) = 11
  • d) DE =  1/2DF = 1/2(50) = 25
  • e) CH =  1/3CF = 1/3(42) = 14
  • b) EF =  DE = 25
  • c) HF =  2/3CF = 2/3(42) = 28
  • f) BE =BH + HE = 22 + 11 = 33

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