Question

На стронах AB, BC, CD и AD квадрат ABCD отмечены соответственно точки A1, B1, C1, D1 так что AA1 = BB1 = CC1 = DD1. Докажите что четырёхугольник A1B1C1D1 квадрат

Answer 1

Доказательство:У квадрата все стороны равны.Сооотвествено это квадрат. Квадрат это фигура у которой все четыре стороны равны

Answer 2

I found some web search results that might help you with your question. Here is a detailed answer based on the information from these sources:

To prove that the quadrilateral A1B1C1D1 is a square, we need to show that it has four equal sides and four right angles. We can use the following facts and properties:

- Since ABCD is a square, it has four right angles and four equal sides. Therefore, AB = BC = CD = AD and ∠ABC = ∠BCD = ∠CDA = ∠DAB = 90°. - Since AA1 = BB1 = CC1 = DD1, we can conclude that A1B1 = B1C1 = C1D1 = D1A1 by subtracting equal segments from equal sides of the square. For example, A1B1 = AB - AA1 = BC - BB1 = B1C1. - Since A1, B1, C1, and D1 are the midpoints of the sides of the square ABCD, we can use the midpoint theorem to show that A1B1 || CD, B1C1 || AD, C1D1 || AB, and D1A1 || BC. For example, A1B1 || CD because A1 and B1 are the midpoints of AB and BC respectively, and AB || CD. - Since A1B1 || CD and B1C1 || AD, we can use the corresponding angles theorem to show that ∠A1B1C1 = ∠CDA and ∠B1C1D1 = ∠DAB. Since ∠CDA and ∠DAB are right angles, we can conclude that ∠A1B1C1 and ∠B1C1D1 are also right angles. Similarly, we can show that ∠C1D1A1 and ∠D1A1B1 are right angles.

Therefore, we have shown that the quadrilateral A1B1C1D1 has four equal sides and four right angles, which means that it is a square. I hope this helps you understand the solution.

Sources: , ,