Answer:The statement If ∠A ≅ ∠C not prove that Δ ABD ≅ Δ CBD by SAS ⇒ CStep-by-step explanation:* Lets revise the cases of congruence - SSS ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ - SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and including angle in the 2nd Δ- ASA ⇒ 2 angles and the side whose joining them in the 1st Δ ≅ 2 angles and the side whose joining them in the 2nd Δ- AAS ⇒ 2 angles and one side in the first triangle ≅ 2 angles and one side in the 2ndΔ- HL ⇒ hypotenuse leg of the first right angle triangle ≅ hypotenuse leg of the 2nd right angle Δ* Lets solve the problem- In the 2 triangles ABD , CBD∵ AB = CB∵ BD is a common side in the two triangles- If AD = CD∴ Δ ABD ≅ Δ CBD ⇒ SSS- If BD bisects ∠ABC∴ m∠ABD = m∠CBD∴ Δ ABD ≅ Δ CBD ⇒ SAS- If ∠A = ∠C∴ Δ ABD not congruent to Δ CBD by SAS because ∠A and ∠C not included between the congruent sides* The statement If ∠A ≅ ∠C not prove that Δ ABD ≅ Δ CBD by SAS