Question

Дано BD -биссектриса угла ABC угол ADB=угол CDB доказать треугольник ABD=треугольник CBD

Answer 1

Треугольники ABD=CBD  равны по второму признаку равенства треугольников: 
по стороне (BD - она общая) и по двум углам (углы ABD=CBD - по условию, так как BD - это биссектриса; углы ADB=CDB - по условию). 

Answer 2

Given Information

The given information states that in triangle ABC, BD is the angle bisector of angle ABC, and angle ADB is equal to angle CDB. The task is to prove that triangle ABD is congruent to triangle CBD.

Proof

To prove that triangle ABD is congruent to triangle CBD, we can use the Angle-Side-Angle (ASA) congruence criterion.

1. Angle ADB = Angle CDB The given information states that angle ADB is equal to angle CDB.

2. Angle ABD = Angle CBD Since BD is the angle bisector of angle ABC, it divides angle ABC into two equal angles, so angle ABD is equal to angle CBD.

3. Side BD is common BD is a common side for both triangles.

By the Angle-Side-Angle (ASA) congruence criterion, we can conclude that triangle ABD is congruent to triangle CBD.

Therefore, the given statement is true, and triangle ABD is indeed congruent to triangle CBD.

Conclusion

The given information has been proven to be true using the Angle-Side-Angle (ASA) congruence criterion.