Question

unit 2 lesson 1 cumulative practice problems

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?

1. complete the following:

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.

1. segments that are congruent have the same length.

Explanation:

Step1: Recall the property of reflection

Reflection is a transformation that maps a figure to its mirror - image. When a figure is reflected, the corresponding parts of the original figure and its image are congruent.

Step2: Analyze the reflection of rectangle \(ABCD\) across line \(EF\)

When rectangle \(ABCD\) is reflected across line \(EF\) to get image \(DCBA\), segment \(AB\) and segment \(DC\) are corresponding parts.

Step3: Use the property of congruent corresponding parts

Since reflection is a congruence transformation, corresponding parts of the original figure and its reflected image are congruent. So, \(AB\cong DC\) because they are corresponding parts of congruent figures (the original rectangle \(ABCD\) and its reflected image \(DCBA\)).

Answer:

Segment \(AB\) is congruent to segment \(DC\) because they are corresponding parts of congruent figures (the original rectangle \(ABCD\) and its reflected image \(DCBA\)).