Explain why a frame that normally is rectangular will, when it sags, keep the shape of a parallelogram.
2007-12-10 12:35:58 · 5 answers · asked by Sally S 1 in Science & Mathematics ➔ Mathematics
It will still have all sides parallel to the opposite one, because the sides don't bend or anything.
2007-12-10 12:41:00 · answer #1 · answered by Snoopy 3 · 0⤊ 0⤋
There are some interesting answers to your question. But in mathematics answers must be based on facts -- definitions, axioms and theorems. Otherwise we have no way to know if the answer someone gives is true or not.
In geometry we can prove -- give accepted reasons for our statements -- that if a quadrilateral has opposite sides equal, both pairs, then that quadrilateral is always a parallelogram. It is easy to prove this using congruent triangles.
So we start with a rectangle. We know that the opposite sides of a rectangle are equal. When the rectangle "sags," by which you mean the right angles get "pushed over" and are no longer right angles, the sides do not change length. So we still have a quadrilateral with opposite sides that are equal and the above theorem states it is therefore a parallelogam.
2007-12-10 12:49:30 · answer #2 · answered by baja_tom 4 · 1⤊ 0⤋
because even if it sags, its still a closed somewhat equal shape
2007-12-10 12:39:16 · answer #3 · answered by Hunter 2 · 0⤊ 0⤋
because the opposite sides are still equals.
2007-12-10 12:42:12 · answer #4 · answered by norman 7 · 0⤊ 0⤋
because its opposite edges remain equal but angles change from right to acute and obtuse.
2007-12-10 12:41:56 · answer #5 · answered by sv 7 · 0⤊ 0⤋