Question

Circles A and V are shown. Line segments A E, A D, and A B are radii. A line is drawn from point B to point C to form a secant. Lines are drawn from point B to point E and from point E to point D to form secants. Line segments V X, V Z and V Y are radii. A line is drawn from point X to point W to form a secant. Lines are drawn from point Y to point Z and from point Z to point X to form secants. Angles B A E and X V Z are congruent.
Given , ⊙A ≅ ⊙V, what congruency statements can you make? Check all that apply.

BC ≅ ZY
Arc B E ≅ Arc Z X
Arc C B ≅ Arc Y Z
∠DAB ≅ ∠ZVX
Arc D E ≅ Arc W X
BE ≅ ZX

Answer 1

Correct choices:
- Arc B E ≅ Arc Z X
- BE ≅ ZX

Explanation: ∠BAE and ∠XVZ are central angles, so they intercept arcs BE and XZ; congruent central angles give congruent arcs, so arc BE ≅ arc ZX. Because the circles are congruent and corresponding arcs are equal, the corresponding chords are equal as well, so chord BE ≅ chord ZX. The other statements do not follow from the given correspondences.