Explain why δadb ≅ δcdb. list the other corresponding parts.

sas, ∠a ≅ ∠c, ≅ , ∠abd ≅ ∠cbd
sas, ∠a ≅ ∠c, ≅ , ∠bda ≅ ∠bdc
sss, ∠a ≅ ∠c, ∠abd ≅ ∠cbd, ∠adb ≅ ∠cdb
asa, ∠a ≅ ∠c, ≅ , ≅

Therefore the Correct option is First one

SAS, ∠A ≅ ∠C,  AB ≅ CB , ∠ABD ≅ ∠CBD .

Step-by-step explanation:

Given:

∠BDA ≅ ∠BDC

AD ≅ CD

TO Prove

ΔADB ≅ ΔCDB

Proof:

In  ΔADB  and ΔCDB  

AD ≅ CD               ……….{Given}

∠BDA ≅ ∠BDC     …………..{Given}

BD ≅ BD               ……….{Reflexive Property}

ΔADB ≅ ΔCDB  ….{By Side-Angle-Side Congruence Postulate}

∴ ∠A ≅ ∠C  {Corresponding Parts of Congruent Triangle are Congruent}

  AB ≅ CB  {Corresponding Parts of Congruent Triangle are Congruent}

∠ABD ≅ ∠CBD {Corresponding Parts of Congruent Triangle are Congruent}

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