Question

congruent.

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.

Explanation:

• Option A: A rectangle has four right angles. There is no information indicating that \(EFGH\) has right angles, so this is incorrect.
• Option B: Just because \(\triangle FEH\) is isosceles (\(\overline{FE}\cong\overline{HE}\)) and \(\triangle FGH\) is its reflection, there is no basis to claim \(EFGH\) has 4 congruent sides.
• Option C: Since \(\triangle FEH\cong\triangle FGH\) (by reflection, which is a congruence transformation), the diagonal \(FH\) will bisect \(\angle EFG\) and \(\angle EHG\) (corresponding angles of congruent triangles).
• Option D: There is no indication from the congruence of \(\triangle FEH\) and \(\triangle FGH\) that \(FH\perp FE\).
• Option E: Because \(\triangle FEH\cong\triangle FGH\) (reflection is a congruence transformation), \(\angle FEH\cong\angle FGH\) (corresponding angles of congruent triangles).

Answer:

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