Question

1 when rectangle abcd is reflected across line ef, the image is dcba.
how do you know that segment ab is congruent to segment dc?
a a rectangle has 2 pairs of parallel sides.
b any 2 sides of a rectangle are congruent.
c congruent parts of congruent figures are corresponding.
d corresponding parts of congruent figures are congruent.
2 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 congruent - figure property for question 1

A reflection is a rigid - motion that produces congruent figures. For rectangle \(ABCD\) and its reflected image \(DCBA\), they are congruent. By the property that corresponding parts of congruent figures are congruent, segment \(AB\) (in rectangle \(ABCD\)) and segment \(DC\) (in rectangle \(DCBA\)) are corresponding parts, so \(AB\cong DC\).

Step2: Analyze congruent - triangle property for question 2

Since \(\triangle FGH\) is the image of \(\triangle FEH\) after a reflection across line \(HF\), \(\triangle FGH\cong\triangle FEH\).

• For option A, just because \(\triangle FGH\cong\triangle FEH\) does not mean \(EFGH\) is a rectangle. There is no information to support this.
• For option B, there is no information to suggest that \(EFGH\) has 4 congruent sides.
• For option C, when \(\triangle FGH\cong\triangle FEH\), the diagonal \(FH\) is the line of reflection. The line of reflection of two congruent triangles (formed by a figure's reflection) bisects the angles at the vertices it passes through. So \(FH\) bisects \(\angle EFG\) and \(\angle EHG\).
• For option D, there is no information to suggest that \(FH\) is perpendicular to \(FE\).
• For option E, since \(\triangle FGH\cong\triangle FEH\), \(\angle FEH\) and \(\angle FGH\) are corresponding angles of congruent triangles, so \(\angle FEH\cong\angle FGH\).

Answer:

1. D. Corresponding parts of congruent figures are congruent.
2. C. Diagonal \(FH\) bisects angles \(EFG\) and \(EHG\); E. Angle \(FEH\) is congruent to angle \(FGH\).