Question

Помогите пожалуйста. В ПАРАЛЕЛЛОГРАММЕ ABCD,биссектрисы углов BиD пересекают диагональ AC в точках Е и F,которые соеденены соответственно с вершинами паралеллограмма В и D. Докажите что четырехугольникBEDF является паралеллограмомм.

Answer 1

Ответ:

если углы соединяются значит то что они четырёхугольники являются парелеллограмомм

Answer 2

Proof that quadrilateral BEDF is a parallelogram

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

Let's consider the given parallelogram ABCD and the points E and F where the bisectors of angles B and D intersect diagonal AC.

Claim 1: Segment BE is parallel to segment DF. Proof: Since the bisectors of angles B and D intersect diagonal AC at points E and F respectively, we can conclude that angles ABE and CDF are congruent. This is because the bisectors of angles B and D divide the angles into two equal parts. Therefore, angle ABE is equal to angle CDF.

Now, let's consider the alternate interior angles ABE and CDF formed by transversal AC.

Claim 2: Segment DE is parallel to segment BF. Proof: Since angles ABE and CDF are congruent, and they are alternate interior angles formed by transversal AC, we can conclude that segment DE is parallel to segment BF. This is because alternate interior angles formed by a transversal and two parallel lines are congruent.

Therefore, we have shown that both segment BE is parallel to segment DF and segment DE is parallel to segment BF. This satisfies the definition of a parallelogram, where opposite sides are parallel.

Hence, we can conclude that quadrilateral BEDF is a parallelogram.

Please let me know if you need any further clarification or assistance.