Question

1. lines x and y are parallel. write an equation that represents the relationship between b and e. explain how you know this equation is always true. (for an equation, use symbols like +, -, =, etc.) 5. trapezoid t and its image t are shown.

\overline{ab}\cong\overline{dc}\cong\overline{de}\cong\overline{gf}
\overline{bc}\cong\overline{fe}
\overline{ad}\cong\overline{gd}
\overline{ad}\perp\overline{gd}
describe a sequence of transformations that take isosceles trapezoid t to its image t.

Explanation:

Step1: Observe common - point

Point \(D\) is common to both trapezoid \(T\) and its image \(T'\).

Step2: Determine rotation

Since \(\overline{AD}\perp\overline{GD}\), trapezoid \(T\) is rotated \(90^{\circ}\) counter - clockwise about point \(D\).

Step3: Check for other transformations

After rotation, no translation or reflection is needed as the sides match up according to the given congruence relations \(\overline{AB}\cong\overline{DC}\cong\overline{DE}\cong\overline{GF}\), \(\overline{BC}\cong\overline{FE}\), \(\overline{AD}\cong\overline{GD}\).

Answer:

Rotate isosceles trapezoid \(T\) \(90^{\circ}\) counter - clockwise about point \(D\).