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What quadrilateral does NOT always have perpendicular diagonals?
rectangleA trapezoid will also suffice.
What are all of the quadrilaterals with perpendicular diagonals?
If a quadrilaterl has a perpendicular diagonas it is a roumbus, also kite has perperndicular diagonals
If one diagonal of a quadrilateral bisects the other then the quadrilateral isa parallelogram?
not necessarily. because the diagonals of a trapezium also bisect each other and it is not a parallelogram. in order for the quadrilateral to become a parallelogram, the opposite angles of it must be equal, and the opposite sides must be equal too. the angles formed by the two diagonals( four in number) also must be equal if they are opposite angles not alternating angles.that's it pal
Why are the diagonals of a square perpendicular bisectors of each other?
You could prove this by congruent triangles, but here are two simpler arguments: --------------- Since a square is a rhombus, and the diagonals of a rhombus are perpendicular bisectors of each other, then the diagonals of a square must be perpendicular bisectors of each other -------------------- A square has four-fold rotational symmetry - as you rotate it around the point where the diagonals cross, there are four positions in which it looks the same. This means that the four angles at the centre must be equal. They will each measure 360/4 = 90 degrees, so the diagonals are perpendicular. Also. the four segments joining the centre to a vertex are all equal, so the diagonals bisect each other.
In which quadrilateral are the diagonals always congruent?
The diagonals of a rhombus are always congruent. A rhombus is a quadrilateral with all sides of equal length. Due to its symmetry, the diagonals of a rhombus bisect each other at right angles, and they are always of the same length. This property distinguishes a rhombus from other quadrilaterals like rectangles or parallelograms.
