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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.
What else can I help you with?
Is the diagonals of a parallelogram the same length?
No, the diagonals of a parallelogram are not necessarily the same length. In a general parallelogram, the diagonals can be of different lengths. However, in a special case of a parallelogram, such as a rectangle or a rhombus, the diagonals may have specific properties, but they are still not equal in a general parallelogram. Only in a rectangle do the diagonals have the same length.
How many diagonals have a rectangle?
It has 2 diagonals
what quadrilateral Has diagonals of different lengths?
A quadrilateral with diagonals of different lengths can be a rectangle or a kite. In a rectangle, the diagonals are equal in length, while in a kite, the diagonals are not equal and intersect at right angles. Other quadrilaterals, like trapezoids and irregular quadrilaterals, can also have diagonals of different lengths. Therefore, many quadrilaterals can fit this description, depending on their specific properties.
How many diagonals of a rectangle?
It ha 2 diagonals
How many diagonals does rectangulo?
A rectangle has 2 diagonals
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.
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
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.
How many diagonals have a rectangle?
It has 2 diagonals
what quadrilateral Has diagonals of different lengths?
A quadrilateral with diagonals of different lengths can be a rectangle or a kite. In a rectangle, the diagonals are equal in length, while in a kite, the diagonals are not equal and intersect at right angles. Other quadrilaterals, like trapezoids and irregular quadrilaterals, can also have diagonals of different lengths. Therefore, many quadrilaterals can fit this description, depending on their specific properties.
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.
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.
