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Is the sum of squares of the sides of a rhombus is equal to sum of square of the diagonals?
Consider a rhombus ABCD, whose diagonals intersect at O.
We know that diagonals of a rhombus bisect each other at 90°, so triangles AOB, AOD, BOC and COD are right angled triangles.
In ΔAOB,
AO2 + OB2 = AB2 (Using Pythagoras theorem)
⇒ AC2 + BD2 = 4AB2
Similarly, AC2 + BD2 = 4BC2
AC2 + BD2 = 4CD2
AC2 + BD2 = 4AD2
Adding all these equations, we get
4(AB2 + BC2 + CD2 + AD2) = 4(AC2 + BD2)
⇒ AB2 + BC2 + CD2 + AD2 = AC2 + BD2
What else can I help you with?
Does a rhombus have equal diagonals?
No. If they were equal the rhombus would become a square.
Does rhombus have equal diagonals?
No. The diagonals of rhombus are not equal.
Are the diagonals of a rhombus equal in lenght?
No. The diagonals of rhombus are not equal.
What is a quadrilateral with diagonals that bisect each other?
The diagonals of any parallelogram (square, rhombus, rectangle, rhomboid) bisect each other. The difference is the the diagonals are equal in length for a square and rectangle, and not equal for a rhombus or rhomboid (oblique diamond).
What is a shape with four sides and perpendicular diagonals?
A shape with four sides and perpendicular diagonals is called a rhombus. In a rhombus, all sides are of equal length, and the diagonals bisect each other at right angles. Additionally, the diagonals are not necessarily of equal length, which distinguishes a rhombus from a square.
Does a rhombus have equal diagonals?
No. If they were equal the rhombus would become a square.
Are the diagonals of a rhombus equal?
No. The diagonals of rhombus are not equal.
Does rhombus have equal diagonals?
No. The diagonals of rhombus are not equal.
Are the diagonals of a rhombus equal in lenght?
No. The diagonals of rhombus are not equal.
Which of the following quadrilaterals have diagonals that are congruent to each other A parallelogram B rectangle C rhombus D square?
'B' and 'D'. The diagonals are equal to each other in rectangles and squares.
What is a quadrilateral with diagonals that bisect each other?
The diagonals of any parallelogram (square, rhombus, rectangle, rhomboid) bisect each other. The difference is the the diagonals are equal in length for a square and rectangle, and not equal for a rhombus or rhomboid (oblique diamond).
What is the relationship between diagonals on a rhombus?
Not in general. The diagonals of a rectangle are equal length. A rhombus that is also a rectangle would be a square.
What is a quadrilateral with equal diagonals and no right angles?
A Rhombus * * * * * WRONG! A rhombus does not have equal diagonals. If it did it would be a square! The shape is a special case of a kite.
How does a square differ from a rhombus?
A square is a rhombus with all angles 90o. When the angles of a rhombus are not all 90o, it differs from the square in this respect, and the diagonals are not of equal length unlike those of a square. A rhombus is like a square in that all its sides are equal in length, opposite sides are parallel and the diagonals are perpendicular and bisect each other.
What is a shape with four sides and perpendicular diagonals?
A shape with four sides and perpendicular diagonals is called a rhombus. In a rhombus, all sides are of equal length, and the diagonals bisect each other at right angles. Additionally, the diagonals are not necessarily of equal length, which distinguishes a rhombus from a square.
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.
Are the diagonals of a rhombus perpendicular and bisect each other?
Yes, they are perpendicular and intersect at their midpoints. The difference between diagonals in a rhombus as opposed to a rectangle or square is that the diagonals are not of equal length.
