If DG is the angle bisector of angle D in the triangle DEF and DE=6 DF=8 EF=10 then EG is
Answers
Answer:
An angle bisector is one that cuts an angle into two equal halves. bearing in mind that a degree has 60 minutes and a minute has 60 seconds, so then 171°30' is just 171 degrees and 30 minutes
Step-by-step explanation:
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Given:
DE=6 units, DF=8 units, EF=10 units
To find:
The length of EG
Solution:
The length of EG is 4.28 units.
We can calculate the length by following the given steps-
We are given that DG is the bisector of angle D.
Point G intersects the side EF.
Let us assume that the length of EG is X.
So, the length of GF=EF-EG
GF=(10-X)
Since DG is an angle bisector, the ratio of DE and DF is equal to the ratio of EG and GF as per the angle bisector theorem.
So, DE/DF=EG/GF.
Using the values,
6/8=X/(10-X)
6(10-X)=X(8)
60-6X=8X
60=8X+6X
60=14X
60/14=X
30/7=X
4.28=X
EG=4.28 units
Therefore, the length of EG is 4.28 units.