Question

1.15.4 crisscross
what happens to the diagonal of a rectangle when the rectangle is reflected across a line of symmetry?
(note: the reflections have already been defined for you. try reflecting either diagonal.)
what does this suggest about the diagonals of rectangles?

Explanation:

Step1: Recall properties of reflection

Reflection is a rigid - motion that preserves distance and angle measures.

Step2: Consider rectangle's symmetry

A rectangle has two lines of symmetry. When reflected across a line of symmetry, corresponding points are equidistant from the line of symmetry.

Step3: Analyze diagonal behavior

The diagonal of the rectangle is mapped onto the other diagonal of the rectangle when reflected across a line of symmetry. This is because the endpoints of the diagonals are symmetric with respect to the lines of symmetry of the rectangle.

Step4: Draw conclusion about diagonals

This suggests that the diagonals of a rectangle are congruent. Since reflection preserves length, and one diagonal can be mapped onto the other, their lengths are equal.

Answer:

The diagonal of the rectangle is mapped onto the other diagonal of the rectangle when reflected across a line of symmetry. This suggests that the diagonals of rectangles are congruent.