Question

Segment DB is a median of ΔADC. Which statement best describes the relationship between triangles ABD and CBD?

A. Triangles ABD and CBD are congruent by the SSS Congruence Postulate.
B. Triangles ABD and CBD are similar by the SSS Similarity Postulate.
C. Triangles ABD and CBD are congruent by the SAS Congruence Postulate.
D. Triangles ABD and CBD are similar by the SAS Similarity Postulate.

Answer 1

HELLO :)

Triangles ABD and CBD are congruent by the SSS Congruence Postulate, this is because both of the triangles have the same angle and the have the same sides. Therefore they are congruent by the SSS Congruence Postulate.

Answer 2

Triangles ABD and CBD are congruent by the SSS Congruence Postulate

⇒ Answer A is the best answer

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.