Question

1. triangle fgh is the image of isosceles triangle feh after a reflection across line fh. select all the statements that are a result of corresponding parts of congruent triangles being congruent.

a efgh is a rectangle.
b efgh has 4 congruent sides.
c diagonal fh bisects angles efg and ehg.
d diagonal fh is perpendicular to side fe.
e angle feh is congruent to angle fgh.

Explanation:

Step1: Analyze option A

Since \( \triangle FEH \) is reflected across line \( FH \) to get \( \triangle FGH \), and \( EFGH \) is formed by these two congruent triangles. In a rectangle, opposite sides are equal and all angles are right - angles. But we have no information to prove \( EFGH \) is a rectangle. So option A is incorrect.

Step2: Analyze option B

\( EFGH \) is formed by two congruent triangles \( \triangle FEH\) and \( \triangle FGH\). A rhombus has 4 congruent sides. There is no information to suggest that \( EF = FG=GH = HE\). So option B is incorrect.

Step3: Analyze option C

Because \( \triangle FEH\cong\triangle FGH\) (by reflection), then \( \angle EFH=\angle GFH\). So diagonal \( FH \) bisects angles \( EFG \) and \( EHG\) (since \( \angle EHG=\angle EFG\) as \( \triangle FEH\cong\triangle FGH\)).

Step4: Analyze option D

There is no information about the slopes of \( FH \) and \( FE \) (or we can't prove the angle between \( FH \) and \( FE\) is \( 90^{\circ}\)) to say that diagonal \( FH \) is perpendicular to side \( FE\). So option D is incorrect.

Step5: Analyze option E

Since \( \triangle FEH\cong\triangle FGH\) (by reflection), then \( \angle FEH=\angle FGH\).

Answer:

C. Diagonal \( FH \) bisects angles \( EFG \) and \( EHG\); E. Angle \( FEH \) is congruent to angle \( FGH\)