line segment AB and CD bisect each other at O . join AC and BD . prove that tringle AOC congruent triangle BOD
To prove that triangle AOC is congruent to triangle BOD, we need to show that they have the same shape and size.
Since line segment AB and CD bisect each other at O, that means that AO is equal to OB and CO is equal to OD. This is because bisecting a line segment divides it into two equal parts.
Now, we need to show that angle AOC is equal to angle BOD. To do this, we can use the fact that when two lines intersect, opposite angles are equal. Since line segments AB and CD bisect each other at O, we can conclude that angle AOB is equal to angle COD.
Therefore, we have:
AO = OB (given)
CO = OD (given)
angle AOC = angle BOD (opposite angles formed by intersecting lines)
By satisfying the Side-Angle-Side (SAS) congruence criterion, we can conclude that triangle AOC is congruent to triangle BOD.