Question

given , $odot a cong odot v$, what congruency statements can you make? check all that apply.$square overline{bc} cong overline{zy}$$square overparen{be} cong overparen{zx}$$square overparen{cb} cong overparen{yz}$$square angle dab cong angle zvx$$square overparen{de} cong overparen{wx}$$square overline{be} cong overline{zx}$

Explanation:

Step1: Recall congruent circle properties

Congruent circles have congruent corresponding radii, arcs, and central angles. We match corresponding parts from $\odot A$ and $\odot V$: $\angle BAE \cong \angle ZVX$ (marked central angles), so their intercepted arcs $\overset{\frown}{BE} \cong \overset{\frown}{ZX}$. Also, we check that $\angle DAB$ and $\angle ZVX$ are not corresponding, and other arcs do not match corresponding circle parts.

Step2: Verify each option

1. $\overline{BC} \cong \overline{ZY}$: No, these are chords with no indication of congruent intercepted arcs.
2. $\overset{\frown}{BE} \cong \overset{\frown}{ZX}$: Yes, corresponding arcs of congruent central angles.
3. $\overset{\frown}{CB} \cong \overset{\frown}{YZ}$: No, no matching central angles or arc markers.
4. $\angle DAB \cong \angle ZVX$: No, $\angle ZVX$ corresponds to $\angle BAE$, not $\angle DAB$.
5. $\overset{\frown}{DE} \cong \overset{\frown}{WX}$: No, no indication these arcs correspond.
6. $\overline{BE} \cong \overline{ZX}$: Yes, chords of congruent arcs in congruent circles are congruent.

Answer:

$\overset{\frown}{BE} \cong \overset{\frown}{ZX}$, $\overline{BE} \cong \overline{ZX}$