Question

review & refresh
tell whether the blue figure is a dilation of the red figure.
1.
2.

Explanation:

1. Check for similarity in shape (for the first pair - pentagons)

Dilation is a transformation that produces similar figures. Similar figures have the same shape but different sizes. The blue pentagon and the red pentagon do not have the same shape (the angles and side - length ratios are not consistent for similar polygons).

2. Check for similarity in shape (for the second pair - parallelograms)

For two parallelograms to be similar (which is a requirement for dilation), the ratios of their corresponding sides must be equal and their corresponding angles must be equal. Let's assume the side lengths of the red parallelogram are \(a,b\) and the side lengths of the blue parallelogram are \(A,B\). If \(\frac{A}{a}=\frac{B}{b}\) and the angles are equal (since in a parallelogram, opposite angles are equal and consecutive angles are supplementary, and if the ratio of sides is constant, by the SSS (side - side - side) similarity criterion for parallelograms (since \(a\parallel b\), \(A\parallel B\), and if \(\frac{A}{a}=\frac{B}{b}\), the parallelograms are similar)).

Answer:

1. No.
2. Yes.