Question

1. trapezoid t and its image t are shown.

describe a sequence of transformations that take isosceles trapezoid t to its image t.
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Explanation:

Step1: Identify the center of rotation

Since $\overline{AD}\cong\overline{GD}$ and $\overline{AD}\perp\overline{GD}$, point $D$ is the center of rotation.

Step2: Determine the angle of rotation

The trapezoid is rotated 180 - degree about point $D$. Because a 180 - degree rotation around a point will map a figure to its opposite - oriented congruent image. And from the congruence of the sides and the perpendicular relationship of $\overline{AD}$ and $\overline{GD}$, a 180 - degree rotation about $D$ will take trapezoid $T$ to $T'$.

Answer:

Rotate trapezoid $T$ 180 degrees counter - clockwise (or clockwise, since 180 - degree rotation is the same in either direction) about point $D$.