Question

a right trapezoid is reflected across the line and then rotated 180 degrees as shown.
select all the statements that are true.
$overline{ab}\cong\overline{jk}$
$overline{ad}\cong\overline{kl}$
$overline{ml}\cong\overline{cb}$
$\angle c\cong\angle l$
$\angle b\cong\angle m$

Explanation:

Step1: Identify rigid transformations

Reflections and 180° rotations are rigid transformations, so they preserve side lengths and angle measures (congruence is maintained between the original and final figure).

Step2: Map corresponding parts

Original trapezoid: $ABCD$; Final trapezoid: $JKML$

• $\overline{AB}$ corresponds to $\overline{JK}$ (right sides of the right trapezoids, preserved by rigid motions)
• $\overline{ML}$ corresponds to $\overline{CB}$ (non-parallel left sides, preserved by rigid motions)
• $\angle C$ corresponds to $\angle L$ (angles at the non-parallel left sides, preserved by rigid motions)
• $\overline{AD}$ does not correspond to $\overline{KL}$ (incorrect mapping of sides)
• $\angle B$ does not correspond to $\angle M$ (incorrect mapping of angles)

Answer:

$\overline{AB}\cong\overline{JK}$, $\overline{ML}\cong\overline{CB}$, $\angle C\cong\angle L$