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.

Explanation:

Step1: Analyze reflection properties

Since reflection across \(HF\) maps \(\triangle FEH\) to \(\triangle FGH\), \(\triangle FEH\cong\triangle FGH\).

Step2: Check each option

• Option A:

For \(EFGH\) to be a rectangle, all angles must be \(90^{\circ}\). There is no information to suggest that \(\angle FEH = 90^{\circ}\) or other angles are \(90^{\circ}\). So, this option is incorrect.

• Option B:

We know \(FE = HE\) (given \(\triangle FEH\) is isosceles) and \(FE=FG\), \(HE = HG\) (by congruence of \(\triangle FEH\) and \(\triangle FGH\)). But we don't know if \(FE = FH\). So, we can't say \(EFGH\) has 4 congruent sides. This option is incorrect.

• Option C:

Because \(\triangle FEH\cong\triangle FGH\), \(\angle EFH=\angle GFH\) and \(\angle EHF=\angle GHF\). So, diagonal \(FH\) bisects angles \(EFG\) and \(EHG\). This option is correct.

• Option D:

There is no information to suggest that \(\angle EFH = 90^{\circ}\). So, we can't say diagonal \(FH\) is perpendicular to side \(FE\). This option is incorrect.

• Option E:

Since \(\triangle FEH\cong\triangle FGH\), by the property of congruent triangles (corresponding parts of congruent triangles are congruent), \(\angle FEH\cong\angle FGH\). This option is correct.

Answer:

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