Given is a quadrilateral ABCD,diagonals AC and BDare such that AO=BO=CO=DO=3cm,where Ois point of intersection of AC and BD then quadrilateral ABCD is a rectangle State true or false with reason
True.
Triangle ABO is congruent to triangle CDO.(Side-angle-side equality) Triangle BCO is congruent to triangle DAO (side-angle-side equality)
Opposite pairs of sides of the quadrilateral are equal in length (due to triangle congruency).
Angles A, B, C and D are right angles.(symmetry requirement)
False.
The statement is false. The given condition of having equal diagonals and equal distances from the intersection point to each vertex does not guarantee that ABCD is a rectangle.
In a rectangle, opposite sides are equal in length and all angles are 90 degrees. This condition is not specified in the given information. So, without additional information about the lengths of the sides or the angles of the quadrilateral, we cannot conclude that ABCD is a rectangle.
False. The statement is false because having all the segments of equal length does not guarantee that a quadrilateral is a rectangle.
To determine if quadrilateral ABCD is a rectangle, we need to consider the properties of a rectangle. A rectangle is a quadrilateral with all angles equal to 90 degrees.
In this case, we are given that the diagonals AC and BD intersect at point O, where AO = BO = CO = DO = 3cm. However, having diagonals of equal length does not necessarily mean that the quadrilateral is a rectangle. There are other quadrilaterals, such as rhombi or squares, that can also have diagonals of equal length but have different angles.
To determine if ABCD is a rectangle, we need additional information, such as the measure of the angles or the relationship between the sides. Without this information, we cannot conclude that ABCD is a rectangle based solely on the given equal lengths of the diagonals.