A Rectangle is a quadrilateral (four sided polygon) with two pairs of equal and parallel sides (opposite sides are parallel and equal, one pair is usually a different length from the other pair but if they are equal it is called a square), and all angles are right angles (90°). It has two diagonals which have the properties:
PROOF of the diagonals congruent:
Take a rectangle ABCD with diagonals AC and BD.
Using Pythagoras on the triangles ACD and BCD:
AC² = AD² + CD²
BD² = BC² + CD²
But as ABCD is a rectangle AD = BC since they are opposite and parallel; thus:
AC² = AD² + CD² = BC² + CD² = BD²
Thus, as AC and BD are the diagonals, they are equal.
Therefore the diagonals of a rectangle are congruent.
True. This can be deduced from the hypotenuse of similar triangles.
True.
It has 2 diagonals
A rectangle has 2 diagonals
It ha 2 diagonals
If the diagonals are cong. then the figure is a rectangle.
The diagonals are equal and they bisect each other.
Properties of rhombus that square has :- * All sides are equal. Properties of rectangle that square has :- *Each angle is 90 degree. *Diagonals are equal.
A rectangle is a square when all of its sides are the same length.A rectangle is SOMETIMES a square.However, a square, is ALWAYS a rectangle.This is due to the properties held by a rectangle as well as properties of a square.Properties of Rectangle:Opposite sides are congruent.All angles are 90o.Opposite sides are parallel.Opposite central angles created by the diagonals are congruent.All diagonals are congruent.Properties of a Square:All sides are congruent.All angles are 90o.Opposite sides are congruent.Opposite sides are parallel.Diagonals intersect at a 90o angle.All diagonals are congruent.So one can have a square that is always a rectangle due to the properties. However, a rectangle will only be a square if properties are the same as a square.SometimesWhen all of its sides are exactly the same length.
Yes the diagonals of a rectangle are equal in lengths
The diagonals of a rectangle bisect the angles only if the rectangle is a square.
This will probably refer to the fact that in a rectangle the diagonals are equal (i.e. have equal length) and they intersect each other in their middle. Moreover, a rectangle is the only quadrangle having this property. So to check that the floor in a room is a rectangle, you just have to draw the diagonals and check the two properties just mentioned.
The diagonals of a rectangle are congruent and they bisect each other.
The diagonals of a rectangle are never perpendicular but the diagonals of a square are perpendicular
It has 2 diagonals
The diagonals of a square are perpendicular whereas the diagonals of a rectangle are not perpendicular.
Yes it does - they bisect each other at the exact centre of the rectangle.
A rectangle has four sides and four angles. A rectangle is a closed shape. All four angles of a rectangle are right angles. That is, they are 90 degrees. Opposite sides of a rectangle are the same length. Opposite sides of a rectangle are parallel. That is, if they were extended infinitely they wouldn't touch. ***Additionally, the diagonals of a rectangle are congruent (unlike other parallelograms), and they also bisect each other. While all parallelograms share the bisecting diagonals characteristic, only rectangles (and by extension squares) have congruent diagonals.***
The diagonals of a rectangle do not cross at right angles