Question

triangle fgh is the image of isosceles triangle feh after a reflection across line hf. fe = he. 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: Recall reflection property

A reflection creates congruent triangles. $\triangle FEH\cong\triangle FGH$.

Step2: Analyze option A

A rectangle has four - right angles. There is no information to suggest $\angle EFG$ or other angles are right angles, so $EFGH$ is not necessarily a rectangle.

Step3: Analyze option B

Just because $\triangle FEH\cong\triangle FGH$ doesn't mean all four sides of $EFGH$ are congruent. We only know about the sides related to the congruent triangles formed by reflection, not all four sides of the quadrilateral.

Step4: Analyze option C

Since $\triangle FEH\cong\triangle FGH$ and $HF$ is the line of reflection, the diagonal $HF$ bisects $\angle EFG$ and $\angle EHG$ due to the symmetry of reflection.

Step5: Analyze option D

There is no information from the congruence of the triangles to suggest that $HF$ is perpendicular to $FE$.

Step6: Analyze option E

Because $\triangle FEH\cong\triangle FGH$, corresponding angles are congruent, so $\angle FEH\cong\angle FGH$.

Answer:

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