Q. 123.7( 3 Votes )
Show that each diagonal of a rhombus bisects the angle through which it passes.
(i) In ΔBOC and ΔDOC
BO = DO [In a rhombus diagonals bisect each other]
CO = CO Common
BC = CD [All sides of a rhombus are equal]
ΔBOC≅ΔDOC [SSS Congurency]
∠BCO =∠DCO from above [corresponding parts of congruent triangles]
Hence, each diagonal of a rhombus bisect the angle through which it passes.
Rate this question :
If the diagonals of a rhombus are 12 cm and 16 cm, find the length of each side.RD Sharma - Mathematics
Construct a rhombus whose diagonals are of length 10 cm and 6 cm.RD Sharma - Mathematics
Fill in the blanks, in each of the following, so as to make the statement true:
(i) A rhombus is a parallelogram in which _______.
(ii) A square is a rhombus in which _________.
(iii) A rhombus has all its sides of ______ length.
(iv) The diagonals of a rhombus _____ each other at ______ angles.
(v) If the diagonals of a parallelogram bisect each other at right angles, then it is a ______.RD Sharma - Mathematics
ABCD is a rhombus. If ∠ACB = 40°, find ∠ADB.RD Sharma - Mathematics
The diagonals of a quadrilateral are perpendicular to each other. Is such a quadrilateral always a rhombus? If your answer is ‘No’, draw a figure to justify your answer.RD Sharma - Mathematics
Which of the following statements are true for a rhombus?
(ii) It has two pairs of equal sides.
(iii) It has only two pairs of equal sides.
(iv) Two of its angles are at right angles.
(v) Its diagonals bisect each other at right angles.
(vi) Its diagonals are equal and perpendicular.
(vii) It has all its sides of equal lengths.
(viii) It is a parallelogram.
(ix) It is a quadrilateral.
(x) It can be a square.
(xi) It is a square.RD Sharma - Mathematics