Answer:
The correct corresponding part is;
[tex]\overline {CB}[/tex] ≅ [tex]\overline {CD}[/tex]
Step-by-step explanation:
The information given symbolically in the diagram are;
ΔCAB is congruent to ΔCED (ΔCAB ≅ ΔCED)
Segment [tex]\overline {CA}[/tex] is congruent to [tex]\overline {CE}[/tex] ( [tex]\overline {CA}[/tex] ≅ [tex]\overline {CE}[/tex])
Segment [tex]\overline {CB}[/tex] is congruent to [tex]\overline {CD}[/tex] ( [tex]\overline {CB}[/tex] ≅ [tex]\overline {CD}[/tex])
From which, we have;
∠A ≅ ∠E by Congruent Parts of Congruent Triangles are Congruent (CPCTC)
∠B ≅ ∠D by CPCTC
Segment [tex]\overline {AB}[/tex] is congruent to [tex]\overline {DE}[/tex] ([tex]\overline {AB}[/tex] ≅ [tex]\overline {DE}[/tex]) by CPCTC
Segment [tex]\overline {AE}[/tex] bisects [tex]\overline {BD}[/tex]
Segment [tex]\overline {BD}[/tex] bisects [tex]\overline {AE}[/tex]
Therefore, the correct option is [tex]\overline {CB}[/tex] ≅ [tex]\overline {CD}[/tex]
