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

Therefore the Correct option is First one

SAS, ∠A ≅ ∠C, AB ≅ CB , ∠ABD ≅ ∠CBD .

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}