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.
Can the following figure be parallelogram. Justify your answer.
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?
ABCD is a parallelogram in which ∠A = 70°. Compute ∠B, ∠C and ∠D.
Which of the following statement is true for a rhombus?
It has two pairs of equal sides.
Which of the following statement is true for a rhombus?
Its diagonals are equal and perpendicular.
Which of the following statement is true for a rhombus?
It has all its sides of equal lengths.
Fill in the blank, inthe following, so as to make the statement true:
A square is a rhombus in which .....
Fill in the blank, inthe following, so as to make the statement true:
A rhombus has all its sides of ...... length.
The diagonals of a parallelogram are not perpendicular. Is it a rhombus? Why or why not?
Which of the following statement is true for a rectangle?
Its diagonals are equal and bisect each other.
Identify all the quadrilateral that have Four sides of equal length
In rhombus ABCD;
(i) if ∠A = 74° ; find ∠B and ∠C.
(ii) if AD = 7.5 cm ; find BC and CD.
ABCD is a rhombus. If ∠BCA = 35°. find ∠ADC.
If the diagonal of a rhombus are equal, then the rhombus is a
A quadrilateral whose all sides are equal, opposite angles are equal and the diagonals bisect each other at right angles is a ______.
If a diagonal of a quadrilateral bisects both the angles, then it is a ______.
