# If a game board is a quadrilateral with diagnols that bisect each other the game board will be a?

Parallelogram (Rectangle, Square, Rhombus, or Rhomboid) or a Kite

### The diagonals of a quadrilateral must bisect each other?

The answer is no the diagonals do not have to bisect each other. That does not necessarily mean that there isn't a quadrilateral that has bisecting diagonals. A quadrilateral is a four-sided polygon which is a close plane figure; in this case with four sides. Meaning that all ends of the straight lines that configure a polygon must connect someway, somehow.

### Conditions which guarantee that a quadrilateral is a parallelogram?

Theorem A: A quadrilateral is a parallelogram if its opposite sides are congruent. Theorem B: A quadrilateral is a parallelogram if a pair of opposite sides is parallel and congruent. Theorem C: A quadrilateral is a parallelogram if its diagonals bisect each other. Theorem D: A quadrilateral is a parallelogram if both pairs of opposite angles are congruent.

### How many diagonals are in a quadrilateral?

A diagonal line of a polygon is a line that joins any two vertices not already joined by a side. A polygon with n sides has n(n-3)/2 diagonals → a quadrilateral with 4 sides has 4(4-3)/2 = 4 × 1 ÷ 2 = 2 diagonal Quadrilaterals include: Squares, rectangles, rhombuses, parallelograms, kites, trapezia (trapezoids). The diagonals of a quadrilateral divide the quadrilateral into 4 triangles. depending upon the quadrilateral some, or all of the triangles…

### Is a quadrilateral with congruent and perpendicular diagonals a square or a rhombus?

It could be a square, but consider the following congruent & perpendicular 'diagonals of a quadrilateral (you will have to connect the endpoints of the diagonals, yourself, as it cannot be drawn in text): . _|___ . | . | . | If the two diagonals, also bisect each other, then it's a square, otherwise it is not.

### Show that if diagonals of a quadrilateral bisects each other then it is a rhombus?

This cannot be proven, because it is not generally true. If the diagonals of a quadrilateral bisect each other, then it is a parallelogram. And conversely, the diagonals of any parallelogram bisect each other. However not every parallelogram is a rhombus. However, if the diagonals are perpendicular bisectors, then we have a rhombus. Consider quadrilateral ABCD, with diagonals intersecting at X, where AC and BD are perpendicular; AX=XC; BX=XD. Then angles AXB, BXC, CXD, DXA…

### 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

### If one side of a quadrilateral is congruent to its opposite side then the quadrilateral is a parallelogram?

No, it doesn't have to be. A quadrilateral can definitely be a parallelogram only if: - Both pairs of opposite sides are parallel. - Both pairs of opposite sides are congruent. - One pair of opposite sides are both congruent and parallel. - Both pairs of opposite angles are congruent. - The diagonals bisect each other.