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Is the sum of squares of the sides of a rhombus is equal to sum of square of the diagonals?
Wiki User
∙ 10y ago
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
Wiki User
∙ 10y ago
No, the sum of squares of the sides of a rhombus is not equal to the sum of squares of the diagonals. The sum of the squares of the sides of a rhombus is equal to four times the square of one side, while the sum of the squares of the diagonals is equal to two times the sum of the squares of the sides.
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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).
Which type of quadilateral has diagonals which are not equal?
Parallelogram, trapezoid, rhombus and a kite are some of them Note that a square and a rectangle have diagonals of equal lengths
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 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.
Which type of quadilateral has diagonals which are not equal?
Parallelogram, trapezoid, rhombus and a kite are some of them Note that a square and a rectangle have diagonals of equal lengths
