Question

1 here is a diagram with two zigzags. (overline{cb}congoverline{fe}), (overline{ba}congoverline{ed}), (angle bcongangle e). write a sequence of rigid motions to take figure (abc) to figure (def). 2 here is a diagram with two circles. (overline{ab}congoverline{cd}). prove the circle centered at (a) is congruent to the circle centered at (c).

Explanation:

Step1: Translate point B to point E

Translate figure ABC so that point B coincides with point E.

Step2: Rotate the figure

Rotate the translated figure around point E so that $\overline{BA}$ coincides with $\overline{ED}$ (since $\overline{BA}\cong\overline{ED}$). Because $\angle B\cong\angle E$, $\overline{CB}$ will coincide with $\overline{FE}$ (since $\overline{CB}\cong\overline{FE}$) and figure ABC will be mapped onto figure DEF.

for question 2:

Step1: Recall the definition of congruent circles

Two circles are congruent if and only if their radii are congruent.

Step2: Identify the radii

In the circle centered at A, $\overline{AB}$ is a radius. In the circle centered at C, $\overline{CD}$ is a radius. Given that $\overline{AB}\cong\overline{CD}$, by the definition of congruent - circles, the circle centered at A is congruent to the circle centered at C.

Answer:

First, translate point B to point E. Then, rotate the translated figure around point E so that $\overline{BA}$ coincides with $\overline{ED}$.