Question

identifying congruent parts
given ( odot a cong odot v ), what congruency statements can you make? choose two correct answers.
( overline{bc} cong overline{zy} )
( overarc{cb} cong overarc{yz} )
( overarc{be} cong overarc{yx} ) (partial, as per image)

Explanation:

Step1: Recall Congruent Circles

Congruent circles have congruent radii and congruent corresponding arcs/chords. Given \( \odot A \cong \odot V \), their radii are equal, and corresponding arcs/chords (matching positions relative to congruent central angles) are congruent.

Step2: Analyze Each Option

• For \( \overline{BC} \cong \overline{ZY} \): Check if \( BC \) (chord of \( \odot A \)) and \( ZY \) (chord of \( \odot V \)) correspond. The central angles (marked red) are congruent, so chords subtended by congruent central angles in congruent circles are congruent. So \( \overline{BC} \cong \overline{ZY} \) is valid.
• For \( \overarc{CB} \cong \overarc{YZ} \): Arcs \( CB \) (of \( \odot A \)) and \( YZ \) (of \( \odot V \)): Since central angles are congruent and circles are congruent, arcs subtended by congruent central angles are congruent. So \( \overarc{CB} \cong \overarc{YZ} \) is valid. (Assuming the third option has a typo, but from visible options, these two make sense.)

Answer:

The two correct answers are:

• \( \overline{BC} \cong \overline{ZY} \)
• \( \overarc{CB} \cong \overarc{YZ} \) (select the checkboxes for these two options)