Math Help - HAIi!,CAN WE FIND LENGTH OF DIAGONALS OF A QUADRILATERAL WHEN ONLY SIDE LENGTHS ARE

GIVEN?

3. Re: HAIi!,CAN WE FIND LENGTH OF DIAGONALS OF A QUADRILATERAL WHEN ONLY SIDE LENGTHS A

The general answer is "No". Imagine taking two sticks of equal length and two other sticks of equal length (not necessarily the same length as the first two). Cut holes at the ends of each stick and tie the sticks together with string so that they can still pivot where the string attaches them. You can then "tilt" the sticks at the pivots to get angles from 0 to 180 degrees at any one pivot. That will give different quadrilaterals (even parallelograms) having the same length sides but different angles and different length diagonals.

That is why triangles are so important in construction- "SSS congruence" tells us that triangles are "rigid" but polygons of more sides are not.

4. Re: HAIi!,CAN WE FIND LENGTH OF DIAGONALS OF A QUADRILATERAL WHEN ONLY SIDE LENGTHS A

Hello, swetha!

I don't suppose you made any sketches . . .

Can we find lengths of diagonals of a quadrilateral when only side lengths are given? .No

Suppose the four side lengths are equal.

We could have a square.
Code:

*  *  *  *  *
* *       * *
*   *   *   *
*     *     *
*   *   *   *
* *       * *
*  *  *  *  *
The diagonals are equal.

Or we could have some rhombus.
Code:

*  *  *  *  *
* *       * *
*   *   *   *
*     *     *
*   *   *   *
* *       * *
*  *  *  *  *
The diagonals are not equal.

The lengths of the sides do not determine
. . the lengths of the diagonals.