Equal triangles ABC and A (1) B (1) C (1) have bisectors BD and B (1) D (1) from vertices B and B (1).

Equal triangles ABC and A (1) B (1) C (1) have bisectors BD and B (1) D (1) from vertices B and B (1). Prove the equality of triangles CBD and C (1) B (1 ) D (1)

Equal triangles ABC AND A (1) B (1) C (1) have bisectors BD and B (1) D (1) from vertices B and B (1). Prove the equality of triangles CBD and C (1) B (1) D (1).

Given: Δ ABC = Δ A1B1C1, BD is the bisector of ABC, B1D1 is the bisector of A1B1C1.

Prove: Δ CBD = Δ С1В1D1 -?

Proof:

Consider Δ CBD and Δ C1В1D1

ВС = В1С1 (by condition, the sides of equal triangles are equal);

∠ BCD = ∠ B1C1D1 (by the condition of the problem, the angles of equal triangles are equal);

∠ DBC = ∠ D1B1C1 (since the bisectors divide the angles by equal angles).

Therefore, according to the second criterion of equality of the triangle, Δ CBD = Δ C1B1D1.

Q.E.D.