Question

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, ≅ , ≅

Answer 1

Answer:

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}