Question

lesson 5
practice problems
1 here is a diagram with two zigzags.
write a sequence of rigid motions to take figure abc to figure def.
2 here is a diagram with two circles.
prove the circle centered at a is congruent to the circle centered at c.
geometry · unit 2 · section a · lesson 5

Explanation:

1.

Step1: Translate segment \(BA\) to segment \(ED\)

Since \(BA\cong ED\), we can perform a translation that maps point \(B\) to point \(E\) and point \(A\) to point \(D\).

Step2: Rotate the translated figure

After the translation, we need to check the orientation. Since \(\angle B\cong\angle E\) and \(CB\cong FE\), we can rotate the translated figure (after Step 1) around point \(E\) (the image of \(B\) after translation) so that segment \(BC\) (now translated) coincides with segment \(EF\).

Step1: Recall the definition of congruent circles

Two circles are congruent if their radii are congruent.

Step2: Identify the radii

In the circle centered at \(A\), \(AB\) is a radius. In the circle centered at \(C\), \(CD\) is a radius. Given that \(AB\cong CD\) (from the problem statement \(\overline{AB}\cong\overline{CD}\)).

Answer:

First, translate figure \(ABC\) so that \(B\) maps to \(E\) and \(A\) maps to \(D\). Then, rotate the translated figure around point \(E\) so that \(BC\) maps to \(EF\).

2.