Question

Дано abcd - параллелограмм ac ∩ bd = {o} доказать BO=OD AO=OC

Answer 1

Доказательство:

1) треугольник AOB и треугольник COD

AB = CD

угол 1 = угол 2 (BD секущ.) AB || CD н.л.

угол 3 = угол 4 (AC секущ.) AB || CD н.л.

треугольник AOB=COD (по 2 призн.)

AO = OC (как соответ. углы)

BO = OD (как соответ. углы)

Answer 2

Given Information:

We are given that ABCD is a parallelogram and that the diagonals AC and BD intersect at point O. We need to prove that BO = OD and AO = OC.

Proof:

To prove that BO = OD, we can use the fact that in a parallelogram, the diagonals bisect each other. This means that the segment BO is equal in length to the segment OD. Similarly, to prove that AO = OC, we can use the same property of parallelograms, which states that the diagonals bisect each other. Therefore, the segment AO is equal in length to the segment OC.

In summary, we have proven that in parallelogram ABCD, BO = OD and AO = OC.

Sources:

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