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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:
- The diagonals are always congruent (of equal length);
- The diagonals bisect each other (cut each other into two equal parts);
- The diagonals do not bisect the angles (unless the rectangle is a square when they do);
- The diagonals are not perpendicular (unless the rectangle is a square when they do).
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.
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How many diagonals have a rectangle?
It has 2 diagonals
How many diagonals does rectangulo?
A rectangle has 2 diagonals
How many diagonals of a rectangle?
It ha 2 diagonals
In a rectangle the diagonals are?
The diagonals are equal and they bisect each other.
What are Parallelogram Are The Diagonals Congruent?
If the diagonals are cong. then the figure is a rectangle.
What are the properties of rhombus and rectangle that square has?
Properties of rhombus that square has :- * All sides are equal. Properties of rectangle that square has :- *Each angle is 90 degree. *Diagonals are equal.
When is a rectangle a square?
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.
Are the diagonals of a rectangle equel?
Yes the diagonals of a rectangle are equal in lengths
Do the diagonals of a rectangle bisect the angles?
The diagonals of a rectangle bisect the angles only if the rectangle is a square.
Use the Rectangle Diagonals Conjecture to determine if the corners of a room are right angles?
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.
What is the Rectangle Diagonals Conjecture?
The diagonals of a rectangle are congruent and they bisect each other.
Are the diagonals of a rectangle sometimes always or never perpendicular?
The diagonals of a rectangle are never perpendicular but the diagonals of a square are perpendicular
How many diagonals have a rectangle?
It has 2 diagonals
What is an attribute of a square that is not an attribute of a rectangle?
The diagonals of a square are perpendicular whereas the diagonals of a rectangle are not perpendicular.
Does a rectangle have diagonals bisect?
Yes it does - they bisect each other at the exact centre of the rectangle.
Do diagonals of the shape rectangle cross at right angles?
The diagonals of a rectangle do not cross at right angles
If the diagonals of a quadrilateral are perpendicular can the quadrilateral be a rectangle?
Sure, a square is a rectangle and the diagonals of a square are perpendicular.
