Question

In a quadrilasteral,

1. If all sides are equal then its a rhombus
2. If all angles are equal then its a rectangle

I know above are true in general. Are these true always ? I mean are there any corner cases where above definitions fail ? If so, could you please draw the quadrilateral and give quick explanation plz..

Answer 1

Hmm, I can't think of any counterexamples.

Answer 2

thank you.. actually those two definitions i figured out just now while revising quadrilaterals. im not sure if they are correct always...

Answer 3

There aren't any counterexamples because those are the very definitions themselves. A rhombus is a quadrilateral with 4 congruent sides. A rectangle is a quadrilateral with 4 congruent angles.

Answer 4

jim thanks for the confirmation

Answer 5

yw

Answer 6

my notes has these for properties of both.


Rectangles are quadrilaterals in which:

1.Both pairs of opposite sides are congruent and parallel.
2.The diagonals bisect each other.
3.Both pairs of opposite angles are congruent.
4.Consecutive angles are supplementary.
5.Contains four right angles.
6.The diagonals are congruent.


Rhombuses are quadrilaterals in which:

1. Both pairs of opposite sides are congruent and parallel.
2.The diagonals bisect each other.
3.Both pairs of opposite angles are congruent.
4.Consecutive angles are supplementary.
5.All four sides are congruent.
6.The diagonals are perpendicular.
7.The diagonals bisect the angles.

Answer 7

feels good to see one single statement defines each of them fully xD

Answer 8

You can shorten things a bit and write that both are parallelograms. A parallelogram is a quadrilateral in which


1.Both pairs of opposite sides are congruent and parallel.
2.The diagonals bisect each other.
3.Both pairs of opposite angles are congruent.
4.Consecutive angles are supplementary.


So basically any rectangle is a parallelogram. Also, any rhombus is a parallelogram. Both are special types of parallelograms.

Answer 9

The short definition of a parallelogram is a quadrilateral in which has opposite sides parallel

Answer 10

yeah that make sense... first four properties are common in both .. .

Answer 11

Oh and a rhombus with 4 congruent angles is a square

so effectively, rhombus + rectangle = square

Answer 12

so that's how they all connect

Answer 13

i see it clearly now thanks so sooo much xD

Answer 14

you're welcome