Please help asap. Question: 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

Diagonal FH bisect angles EFG and EHG and the angle FEH is congruent to angle FGH.

The diagram is given the question.

We need to check all the statements that are applicable for the diagram.

1) EFGH is a rectangle.

The above statements is not true in general. EFGH is a quadrilateral with opposites sides are equal, it may be rectangle in some cases but it is not always be a rectangle.

2). EFGH has 4 congruent sides.

The above statement is also false. EFGH has two opposite sides are congruent.

3). Diagonal FH bisect angles EFG and EHG.

The above statement is true. Triangle EFH and FGH both are isosceles triangles and hence they both have equal angles for the equal sides. Thus, it is true in all cases.

4). Diagonal FH is perpendicular to side Fe.

The above case is not true in general.

5). Angle FEH is congruent to angle FGH.

Yes, the above statement is the correct one, because both the triangles are congruent to each other.

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Options (2), (3) and (5)

Step-by-step explanation:

ΔFGH is the image of isosceles triangle ΔFEH.

Option 1.

EFGH is a rectangle.

False.

(Since measures of all angles are not known)

Option (2).

EFGH has 4 congruent sides.

True.

Option (3).

Diagonal FH bisects angle EFG and EHG.

True.

(Since, ΔFGH is the image of ΔFEH, therefore, both the parts of EFGH will be equal)

Option (4).

Diagonal FH is perpendicular to side FE.

False.

(Since measure of all angles are not known).

Option (5).

∠FEH ≅ ∠FGH

True.

(Since, ΔFEH and  ΔFGH are the image of each other. Therefore, both the triangles will be congruent)

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