Question

state the theorem that proves the triangles are congruent. then, select the correct congruence statement for the triangles. point ( f ) is the midpoint of ( overline{d g} ) and ( overline{e h} ). move each correct answer into the spaces provided. congruence theorem the congruence statement is

Explanation:

Step1: Use the mid - point property

Since \(F\) is the mid - point of \(\overline{DG}\), \(DF = FG\). Since \(F\) is the mid - point of \(\overline{EH}\), \(FH=FE\). Also, \(\angle DFH=\angle EFG\) (vertically opposite angles).

Step2: Apply the congruence theorem

By the Side - Angle - Side (SAS) congruence theorem (two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle), \(\triangle DFH\cong\triangle GFE\).

Answer:

Congruence Theorem: SAS (Side - Angle - Side)
The congruence statement is \(\triangle DFH\cong\triangle GFE\)