Based on the given information, we know that line segment DF bisects angle EDG. This means that angle EDF is congruent to angle GDF.
Since angle EDF and angle GDF are congruent, we can set up an equation:
angle EDF + angle GDF = 180 degrees
If we let angle EDF be x degrees, then angle GDF is also x degrees.
So we have:
x + x = 180
2x = 180
x = 90
Since angle EDF is 90 degrees, we can conclude that angle EDF is a right angle.
Now, we can see that triangle DFG is a right triangle with right angle at angle D. If angle EDF is a right angle, then angle F is also a right angle.
Therefore, triangle DFG is a right triangle with right angles at D and F.
Since triangle DFG is a right triangle, we can apply the Pythagorean Theorem:
DF^2 + FG^2 = DG^2
However, we do not have enough information to find the values of DF, FG, and DG. The length of FG cannot be determined without additional information.
DF−→−
bisects ∠EDG
. Find FG. The diagram is not to scale.
A diagram of two triangles drawn in the interior of an angle is shown. Angle upper E upper D upper G is shown with point upper F located in the interior of the angle. Point upper F is connected to point upper D with a line segment. Angle upper E upper D upper F and angle upper G upper D upper F both are lab
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