Question

1. triangle fgh is the image of isosceles triangle feh after a reflection across line hf. 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.
fe ≅ he

Explanation:

Step1: Recall properties of reflection

A reflection is a rigid - motion that preserves congruence. $\triangle FEH\cong\triangle FGH$ since $\triangle FGH$ is the image of $\triangle FEH$ after reflection across line $HF$.

Step2: Analyze option A

Just because $\triangle FEH\cong\triangle FGH$, we cannot conclude that $EFGH$ is a rectangle. There is no information about right - angles, so A is incorrect.

Step3: Analyze option B

We cannot conclude that $EFGH$ has 4 congruent sides. There is no information to support this, so B is incorrect.

Step4: Analyze option C

Since $\triangle FEH\cong\triangle FGH$ and reflection across line $HF$ is the transformation, diagonal $FH$ is the axis of symmetry. So, diagonal $FH$ bisects angles $EFG$ and $EHG$. C is correct.

Step5: Analyze option D

There is no information to suggest that diagonal $FH$ is perpendicular to side $FE$. So, D is incorrect.

Step6: Analyze option E

Since $\triangle FEH\cong\triangle FGH$, corresponding angles are congruent. $\angle FEH$ and $\angle FGH$ are corresponding angles, so $\angle FEH\cong\angle FGH$. E is correct.

Answer:

C. Diagonal $FH$ bisects angles $EFG$ and $EHG$.
E. Angle $FEH$ is congruent to angle $FGH$.