Question

Отрезки AB и CD равны и пересекаются в точке O так, что AO=OD. Доказать, что BD=AC.

Answer 1

1.АВ=СД(по условию),АО=СД(по усл.),из этих двух следует,что СО=ОВ.

2.АВ=СД(по усл.),Углы:АОС=ВОД(верт.),СО=ОВ(по доказ.),из этих трёх следует,что треугольники:АОС=ДОВ(по первому пр.равенства тр.),раз треугольники равные,то равны и соответствующие стороны:АС=ДВ.

Answer 2

Given Information:

We are given that there are two line segments, AB and CD, which are equal in length and intersect at point O. Additionally, it is given that AO is equal to OD.

To Prove:

We need to prove that BD is equal to AC.

Proof:

To prove that BD is equal to AC, we can use the fact that the line segments AB and CD are equal in length and that AO is equal to OD.

Let's consider the triangles ABO and CDO. Since AB and CD are equal in length, we can conclude that AO is equal to CO (as they are opposite sides of the triangle). Similarly, OD is equal to BO.

Now, let's consider the triangles ACO and BDO. We know that AO is equal to CO and OD is equal to BO. Additionally, we have AO = OD. Therefore, we can conclude that triangle ACO is congruent to triangle BDO by the Side-Side-Side (SSS) congruence criterion.

By congruence, we know that the corresponding sides of congruent triangles are equal. Therefore, we can conclude that AC is equal to BD.

Hence, we have proved that BD is equal to AC.

Note: The proof provided above is based on the given information and the congruence of triangles ACO and BDO.