Question

Дано. BC||AD; Угол BAC = Углу DCA. Доказать. ABCD - Параллелограмм.

Answer 1

Углы диагонали равны как накрест лежащие, следовательно стороны АВ и DC параллельны

четырехугольник, у которого стороны попарно параллельны, называется параллелограммом.

Answer 2

Given Information:

We are given that BC || AD and that angle BAC = angle DCA. We need to prove that ABCD is a parallelogram.

Proof:

To prove that ABCD is a parallelogram, we need to show that opposite sides are parallel.

Let's consider the given information and use it to prove that ABCD is a parallelogram.

From the given information, we know that BC || AD. This means that BC and AD are parallel.

We also know that angle BAC = angle DCA. This implies that angle BAC and angle DCA are congruent.

To prove that ABCD is a parallelogram, we need to show that opposite sides are parallel. Let's consider the opposite sides of ABCD:

1. Side AB: Since BC || AD, we can conclude that side AB is parallel to side CD.

2. Side AD: Since BC || AD, we can conclude that side AD is parallel to side BC.

Therefore, we have shown that opposite sides of ABCD are parallel, which means that ABCD is a parallelogram.

Conclusion:

Based on the given information and the proof provided, we can conclude that ABCD is a parallelogram.

Note: The sources provided do not directly address the given problem. However, the proof is based on the properties of parallel lines and congruent angles, which are well-known geometric concepts.