Answer:
Triangles ABD and CBD are congruent by the SSS Congruence Postulate
⇒ Answer A is the best answer
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 ΔADC
∵ DA = DC
∵ DB is a median
- The median of a triangle is a segment drawn from a vertex to the
mid-point of the opposite side of this vertex
∴ B is the mid-point of side AC
∴ AB = BC
- In the two triangles ABD and CBD
∵ AD = CD ⇒ given
∵ AB = CB ⇒ proved
∵ BD = BD ⇒ common side in the two triangles
∴ The two triangles are congruent by SSS
* Triangles ABD and CBD are congruent by the SSS Congruence
Postulate.
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