A line that intersects another line segment and divides into two equal parts is known as a bisector. A line connecting two opposite corners is called diagonals. In this article, we are proving that the Diagonals of a Parallelogram Bisect Each Other. So, the students of grade 9 who are unable to understand the concept of the properties of a parallelogram can use this page and learn the theorem clearly. The use of theorem is that you can understand how it is proved and solve any type of problem in the exams.
- Pair of Opposite Sides of a Parallelogram are Equal and Parallel
- A Parallelogram, whose Diagonals are of Equal Length, is a Rectangle
Diagonals of a Parallelogram Bisect Each Other Proof
Statement: Prove that the diagonals of a parallelogram bisect each other.
Given a Parallelogram ABCD and we will prove that the diagonals bisect each other into equal parts. First, we will join the diagonals and name the intersection point at O. Angle OCD and OBA are equal in measure because the lines CD and BA are parallel and that makes them alternate angles. The lengths AB and CD are equal and opposite. Triangle ABO and COD are congruent.
AD || BC
AD = BC [opposite sides of a parallelogram are equal]
∠OBC ≅ ∠ODA [Alternate interior angles]
∠OCB ≅ ∠OAD [Alternate interior angles]
ΔOBC ≅ ΔODA
OB = OD [corresponding angles in congruent triangles]
OA = OC [corresponding angles in congruent triangles]
Therefore the diagonals of a parallelogram do bisect each other into equal parts.
FAQs on Diagonals of a Parallelogram Bisect Each Other
1. Why do the diagonals of a parallelogram bisect each other?
In any parallelogram, the diagonals (line segment connecting the opposite corners) bisect each other. That is each diagonal cuts the other into two equal parts.
2. Does the diagonals of a parallelogram bisect each other at right angles?
The sum of the other two interior angles in both the triangles should be equal to 90 degrees. Hence, the diagonals of a parallelogram bisect each other but not necessarily at right angles.
3. Are diagonals of parallelogram equal?
The diagonals of a parallelogram are not equal. The opposite sides and opposite angles of a parallelogram are equal.