Advertisements
Advertisements
प्रश्न
Diagonals of a parallelogram intersect each other at point O. If AO = 5, BO = 12 and AB = 13 then show that `square`ABCD is a rhombus.
Advertisements
उत्तर
Given: AO = 5, BO = 12 and AB = 13
To Prove: `square`ABCD is a rhombus.
Proof:
AO2 + BO2
= 52 + 122
= 25 + 144
= 169 ...(i)
∴ AB2 = 132 = 169 ...(ii)
∴ AB2 = AO2 + BO2 ...[From (i) and (ii)]
∴ ∆AOB is a right-angled triangle. ...[Converse of Pythagoras theorem]
∴ ∠AOB = 90°
∴ seg AC ⊥ seg BD ...(iii) [A-O-C]
∴ In parallelogram ABCD,
∴ seg AC ⊥ seg BD ...[From (iii)]
∴ `square`ABCD is a rhombus. ...[A parallelogram is a rhombus perpendicular to each other]
APPEARS IN
संबंधित प्रश्न
The following figure is parallelogram. Find the degree values of the unknowns x, y, z.
The following figure is parallelogram. Find the degree values of the unknown x, y, z.
The following figure is parallelogram. Find the degree values of the unknown x, y, z.
In the following figure RISK and CLUE are parallelograms. Find the measure of x.
The measure of one angle of a parallelogram is 70°. What are the measures of the remaining angles?
Two adjacent angles of a parallelogram are as 1 : 2. Find the measures of all the angles of the parallelogram.
Two adjacent sides of a parallelogram are 4 cm and 3 cm respectively. Find its perimeter.
Points E and F lie on diagonal AC of a parallelogram ABCD such that AE = CF. What type of quadrilateral is BFDE?
Which of the following statement is true for a rhombus?
It has two pairs of parallel sides.
Which of the following statement is true for a rhombus?
It is a square.
If the diagonals of a rhombus are 12 cm and 16cm, find the length of each side.
Diagonals of a rhombus are 20 cm and 21 cm respectively, then find the side of rhombus and its perimeter.
State with reason whether the following statement is ‘true’ or ‘false’.
Every rhombus is a rectangle.
If opposite angles of a rhombus are (2x)° and (3x - 40)° then value of x is ______.
If the adjacent sides of a parallelogram are equal then parallelogram is a ______.
In a rhombus diagonals intersect at ______ angles.
A rhombus is a parallelogram in which ______ sides are equal.
All rhombuses are squares.
Diagonals of a quadrilateral are perpendicular to each other. Is such a quadrilateral always a rhombus? Give a figure to justify your answer.
