Question

Отрезок РL и отрезок ЕК пересекаются в их середине М. Докажите, что прямая РК параллельна прямой ЕL. Заранее спасибо

Answer 1

Отрезок РЛ и ЕК, ЕМ=МК, РМ=МЛ, треугольник ЕМЛ=треугольник РМК по двум сторонам и углу между ними (уголЕМЛ=уголРМК как вертикальные), тогда уголР=уголЛ - это внутренние разносторонние углы, если при пересечении двух прямых (ЕЛ и РК) третьей прямой (РЛ) внутренние разносторонние углы равны, то прямые параллельны - ЕЛ параллельна РК

Answer 2

Proof of Parallel Lines

To prove that line RK is parallel to line EL, given that segment PL and segment EK intersect at their midpoint M, we can use the property that if a line is drawn through the midpoint of one side of a triangle parallel to another side, it will bisect the third side.

Proof: 1. Given that segment PL and segment EK intersect at their midpoint M. 2. We want to prove that line RK is parallel to line EL.

Let's consider the triangles formed by these segments and their midpoints.

In triangle PML, M is the midpoint of PL, and in triangle EMK, M is the midpoint of EK.

According to the property mentioned earlier, if we draw a line through the midpoint of one side of a triangle parallel to another side, it will bisect the third side.

So, if line RK is parallel to line EL, then it will bisect segment PE.

This can be proven by the midpoint theorem, which states that a line segment joining the midpoints of two sides of a triangle is parallel to the third side and half of its length.

Therefore, by proving that line RK bisects segment PE, we can conclude that line RK is parallel to line EL.

This proof demonstrates that the given conditions lead to the conclusion that line RK is parallel to line EL.