The diagonals of a parallelogram bisect each other.
Text Solution
Verified by Experts
We have to prove diagonals of parallelogram ABCD bisects each other.
i.e, `OA=OC & OB=OD`
Now In `ΔAOD and ΔBOC`
`AD=BC` [opposite sides are equal]
`∠ADO=∠CBO` [alternate interior angle]
Similarly `∠DAO=∠BCO`
`ΔAOD≅ΔBOC` by (ASA rule)
So,
...
|
Topper's Solved these Questions
NCERT THEOREMS
NCERT ENGLISH|Exercise THEOREM 8.7|1 Videos
NCERT THEOREMS
NCERT ENGLISH|Exercise THEOREM 8.8|1 Videos
NCERT THEOREMS
NCERT ENGLISH|Exercise THEOREM 8.5|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
if diagonals of a parallelogram bisect each other,prove that its a rhombus
The diagonals of a quadrilateral bisect each other. This quadrilateral is a (a) rectangle (b) kite (c) trapezium (d) none of these
State 'True' or 'False' The diagonals of a quadrilateral bisect each other
Prove using vectors: The diagonals of a quadrilateral bisect each other iff it is a parallelogram.
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
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.
If diagonal of a parallelogram bisects one of the angles of the parallelogram, it also bisects the second angle.
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
Prove that; If the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.
Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.
