If the diagonals of a quadrilateral bisect each other, then the
quadrilateral is a parallelogram.
Text Solution
Verified by Experts
In `/_\AOD` and `/_\COB`
`OA=OC` (given)
`/_AOD=/_COB` (vertically opposite angles)
`OD=OB` (given)
Thus, by SAS congruency, `/_\AOD` and `/_\COB` are congruent.
Therefore, `/_OAD=/_OCB`
For lines `AB` and `CD` with transversal `BD`,
...
Topper's Solved these Questions
NCERT THEOREMS
NCERT ENGLISH|Exercise THEOREM 8.8|1 Videos
NCERT THEOREMS
NCERT ENGLISH|Exercise THEOREM 8.9|1 Videos
NCERT THEOREMS
NCERT ENGLISH|Exercise THEOREM 8.6|1 Videos
LINES AND ANGLES
NCERT ENGLISH|Exercise Exercise 6.1|6 Videos
NUMBER SYSTEMS
NCERT ENGLISH|Exercise EXERCISE 1.4|2 Videos
Similar Questions
Explore conceptually related problems
Given statements in (a) and (b). Identify the statements given below as contrapositive or converse of each other.(a) If you live in Delhi, then you have winter clothes. (i) If you do not have winter clothes, then you do not live in Delhi. (ii) If you have winter clothes, then you live in Delhi.(b) If a quadrilateral is a parallelogram, then its diagonals bisect each other. (i) If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram. (ii) If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
State True or False If the diagonals of a quadrilateral bisect each other at right angle, the quadrilateral is a square.
If the diagonals of a quadrilateral bisect each other at right angle, then the quadrilateral is a (a) parallelogram (b) rectangle (c) rhombus (d) kite
The diagonals of a parallelogram bisect each other.
The diagonals of a rectangle bisect each other
Prove using vectors: The diagonals of a quadrilateral bisect each other iff it is a parallelogram.
Prove that; If the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.
If the diagonals of a quadrilateral bisect each other at right angle, prove that the quadrilateral is a rhombus. A rhombus has all its four sides equal.
If one diagonal of a quadrilateral bisects the other, then it also bisects the quadrilateral.
Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.
