Question

7HELP________________

Answer 1

Answer:

The statement If ∠A ≅ ∠C not prove that Δ ABD ≅ Δ CBD by SAS ⇒ C

Step-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