State true or false:
The figure formed by joining the mid-points of the consecutive sides of a quadrilateral is Parallelogram.
The correct option is A True
True
When you connect the consecutive midpoints of a quadrilateral, another quadrilateral is formed inside of it. We will call the original figure the mother figure and this new figure the daughter figure. To determine what the daughter is, you must examine the diagonals of the mother. It is possible to use the diagonals of the mother because the diagonals are parallel to the sides of the daughter.
The type of quadrilateral that is formed can either be a rhombus, a rectangle, or a square, but it will always be a parallelogram. This is because when the midpoints are connected to form the sides of the daughter figure, each side of the mother figure is bisected. Each newly formed side will be parallel to a diagonal of the mother. Two of the newly formed sides are parallel to the same diagonal and therefore are parallel to each other. Along with the other two sides of the daughter that are parallel to the other diagonal of the mother, a parallelogram is formed.
True
When you connect the consecutive midpoints of a quadrilateral, another quadrilateral is formed inside of it. We will call the original figure the mother figure and this new figure the daughter figure. To determine what the daughter is, you must examine the diagonals of the mother. It is possible to use the diagonals of the mother because the diagonals are parallel to the sides of the daughter.
The type of quadrilateral that is formed can either be a rhombus, a rectangle, or a square, but it will always be a parallelogram. This is because when the midpoints are connected to form the sides of the daughter figure, each side of the mother figure is bisected. Each newly formed side will be parallel to a diagonal of the mother. Two of the newly formed sides are parallel to the same diagonal and therefore are parallel to each other. Along with the other two sides of the daughter that are parallel to the other diagonal of the mother, a parallelogram is formed.
