Connect with a knowledgeable community and get your questions answered on IDNLearn.com. Ask any question and receive accurate, in-depth responses from our dedicated team of experts.
Sagot :
Given the Centroid postulate:
The centroid is two-thirds of the distance from each vertex to the midpoint of the opposite side.
Each median is split into two parts such that the longer part is twice the length of the shorter part.
In this case, we have that:
AG= 10 ---> 2/3 (longer part) so, EG= (10/2/3) *1/3 = 5--> EG=5
CD=18 ----> 3/3 (total part) so, DG= 18*1/3= 6 (shorter part) and CG= 18*2/3=12 (longer part)
Now, we need to calculate BF, in this case, we know that sides AD and DB are congruent by Centroid postulate, so in order to calculate the unknown side BF, we can use the Pythagoras Theorem:
DB=8
DG = 6
BG is the Hypothenuse
--> BG^2 = DB^2 + DG^2 = 8^2 + 6^2
--> BG = sqrt[8^2+6^2]= 10
So, BG= 10
Now, in order to calculate the left side GF, we must consider that BG is the longer part and GF is the shorter part.
So BG=10----> 2/3 Total part = 10/(2/3) = 15 ---> GF = 15-10 = 5
ANSWERS:
BD = 8
AE=AG+EG=10+5= 15
AB=AD+DB=8+8 = 16
CG= 12
EG=5
DG=6
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. IDNLearn.com is your reliable source for answers. We appreciate your visit and look forward to assisting you again soon.
