Question

Треугольники АВС и BAD равны, причём точки С и D лежат по разные стороны от прямой АВ. Докажите, что треугольник CBD и DAC равны. С обьяснениями пожалуйста

Answer 1

Т.к. ΔАВС = ΔABD, то АС = BD, CB = AD, ∠CAO = ∠OBD.

В ΔCBD и ΔDAC: CD — общая

АС = DB, AD = CB (из условия).

Таким образом, ΔCBD = ΔDAC по 3-му признаку равенства треугольников, таким образом, ∠CDB = ∠DCA.

Answer 2

Given Information

We are given that triangles ABC and BAD are congruent, and points C and D lie on opposite sides of the line AB.

Proof of Triangle CBD and DAC Congruence

To prove that triangles CBD and DAC are congruent, we can use the Side-Angle-Side (SAS) congruence criterion.

1. Side CB is congruent to side DA: - Since triangles ABC and BAD are congruent, we know that side AB is congruent to side BA. - Therefore, side CB is congruent to side DA.

2. Angle CBD is congruent to angle DAC: - Since triangles ABC and BAD are congruent, we know that angle ABC is congruent to angle BAD. - Therefore, angle CBD is congruent to angle DAC.

3. Side BD is congruent to itself.

By the SAS congruence criterion, we have shown that triangles CBD and DAC are congruent.

Conclusion

Therefore, we have proved that triangles CBD and DAC are congruent using the Side-Angle-Side (SAS) congruence criterion.

Please let me know if I can help you with anything else.