Q3 of 13 Page 96

Line segments AB and CD bisect each other at O. Let’s prove that AC and BD are parallel. Let’s write what kind of quadrilateral is ABCD.


Given here two line segments AB and CD bisects each other at O.


∴ OA=OB and OC=OD


Now, in ∆AOC and ∆BOD,


∠AOC=∠BOD (vertically opposite angles)


OC=OD (given)


OA=OB (given)


∴ ∆AOC ≅ ∆BOD (by SAS rule)


∠ACO=∠ODB (by cpct )


∠CAO=∠OBD (by cpct )


But these are also the alternate interior angles.


So, AC||BD


Similarly, ∆AOD ≅ ∆BOC


And AD||BC


Hence ACBD is a parallelogram.


More from this chapter

All 13 →
2 A

let’s see the isosceles triangles below and without measuring let’s write which angles are equal in measurement in each triangle.


 2 B

let’s see the isosceles triangles below and without measuring let’s write which angles are equal in measurement in each triangle.


 4

E and F are twp points on two parallel straight-line AB and CD respectively. O is the midpoint of line segment EF. We draw a straight line passing through O which intersect AB and CD at P and Q respectively. Let’s prove that O bisects the line segment PQ.

 5

If we produce the base of an isosceles triangle in both sides then two exterior angles formed. Let’s prove that they are equal in measurement.