Question

В параллелограмме АВСК диагонали пересекаются в точке О, М середина ВО, Р середина КО. Докажите что АМСР параллелограмм.

Answer 1

В параллелограмме диагонали тоской пересечения делятся пополам -
РО=ОМ и АО=ОС значит АМСР параллелограмм по свойству параллелограмма

Answer 2

Proof that AMRS is a Parallelogram

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

Given: - In parallelogram ABCD, the diagonals AC and BD intersect at point O. - Point M is the midpoint of segment BO. - Point R is the midpoint of segment CO.

To prove that AMRS is a parallelogram, we will show that opposite sides are parallel.

Step 1: Let's consider segment AM and segment RS.

Step 2: Since M is the midpoint of segment BO and R is the midpoint of segment CO, we can conclude that segment MR is parallel to segment BC. This is because the midpoints of a line segment divide it into two equal parts, and the line connecting the midpoints is parallel to the line segment.

Step 3: Now, let's consider triangle ABO and triangle CRO.

Step 4: By the midpoint theorem, we know that segment AM is parallel to segment CR, and segment AB is parallel to segment CO.

Step 5: Since segment AM is parallel to segment CR and segment AB is parallel to segment CO, we can conclude that triangle ABO is similar to triangle CRO by the AA (Angle-Angle) similarity criterion.

Step 6: As a