Question

given, ⊙a≅⊙v, what congruency statements can you make? check all that apply.
□ bc≅zy
□ be≅zx
□ cb≅yz
□ ∠dab≅∠zvx
□ de≅wx
□ be≅zx

Explanation:

Step1: Recall congruent - circle properties

If two circles $\odot A\cong\odot V$, corresponding chords, arcs, and central - angles are congruent.

Step2: Analyze each option

• For $\overline{BC}\cong\overline{ZY}$: There is no information to suggest that these chords are corresponding chords in the congruent circles, so this is not necessarily true.
• For $\overset{\frown}{BE}\cong\overset{\frown}{ZX}$: Since the circles are congruent and these are corresponding arcs (assuming they subtend equal central - angles or are in corresponding positions), this is a valid congruency statement.
• For $\overset{\frown}{CB}\cong\overset{\frown}{YZ}$: There is no information to suggest that these arcs are corresponding arcs in the congruent circles, so this is not necessarily true.
• For $\angle DAB\cong\angle ZVX$: Since the circles are congruent, corresponding central - angles are congruent. If $\angle DAB$ and $\angle ZVX$ are central - angles in the congruent circles $\odot A$ and $\odot V$ respectively, this is a valid congruency statement.
• For $\overline{DE}\cong\overline{WX}$: There is no information to suggest that these chords are corresponding chords in the congruent circles, so this is not necessarily true.
• For $\overline{BE}\cong\overline{ZX}$: Since the circles are congruent and these are corresponding chords (assuming they subtend equal central - angles or are in corresponding positions), this is a valid congruency statement.

Answer:

$\overline{BE}\cong\overline{ZX}$, $\overset{\frown}{BE}\cong\overset{\frown}{ZX}$, $\angle DAB\cong\angle ZVX$