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. (lesson 2 - 1) a. efgh is a rectangle. b. efgh is a rhombus. c. diagonal fh bisects angles efg and ehg. d. diagonal fh is perpendicular to side fe. e. angle ehf is congruent to angle fgh. f. angle feh is congruent to angle fgh.

Explanation:

Step1: Recall properties of congruent triangles after reflection

Since $\triangle FEH\cong\triangle FGH$ (by reflection), corresponding - parts are congruent.

Step2: Analyze option A

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

Step3: Analyze option B

Just from the congruence of the two triangles, we cannot say that $EFGH$ is a rhombus. We don't know if all sides are equal, so B is incorrect.

Step4: Analyze option C

Since $\triangle FEH\cong\triangle FGH$ and $FH$ is the line of reflection, $FH$ is the axis of symmetry for the combined figure $EFGH$. So, diagonal $FH$ bisects angles $EFG$ and $EHG$. C is correct.

Step5: Analyze option D

There is no information from the congruence of the triangles to suggest that $FH$ is perpendicular to $FE$. So, D is incorrect.

Step6: Analyze option E

$\angle EHF$ and $\angle FGH$ are not corresponding angles of congruent triangles $\triangle FEH$ and $\triangle FGH$. So, E is incorrect.

Step7: Analyze option F

Since $\triangle FEH\cong\triangle FGH$, by the property of corresponding parts of congruent triangles, $\angle FEH\cong\angle FGH$. F is correct.

Answer:

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