In triangle DEF, angle E is equal to angle F, which also implies that the sides opposite each of them are also congruent based on the angle-side relationship theorem . Therefore the statement that will be true is:
C. [tex]\mathbf{\overline{FD} \cong \overline{ED}}[/tex]
Recall:
The angle-side relationship theorem states that the length of all sides of a triangle is relative to the size of the angles directly opposite to them.
Thus,
Angle F = 180 - (61 + 58) (sum of triangle)
Angle F = 61 degrees
<F and < E are congruent to each other since m<E = 61 degrees.
By implication, the sides opposite to each of the angles will also be congruent to each other.
Therefore, [tex]\mathbf{\overline{FD} \cong \overline{ED}}[/tex] because [tex]\angle E \cong \angle F[/tex]
In conclusion, in triangle DEF, angle E is equal to angle F, which also implies that the sides opposite each of them are also congruent based on the angle-side relationship theorem . Therefore the statement that will be true is:
C. [tex]\mathbf{\overline{FD} \cong \overline{ED}}[/tex]
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