Question

How far down (from a vertex) along each diagonal do the diagonals of a parallelogram intersect?

Answer 1

Solution :

To answer our question, we first understand what is a Parallelogram.

Definition of a Parallelogram:

In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides.

Now we also understand the properties of a parallelogram

Let us consider a Parallelogram ABCD, with AB ∥ DC and AB ∥ BC

Join A to C to form one diagonal AC, join B to D to form another diagonal BD. Let the intersection point of diagonal AC and BD be O.

Properties of a Parallelogram:

1. Opposite sides are congruent (AB = DC).
2. Opposite angels are congruent (D = B).
3. Consecutive angles are supplementary (A + D = 180°).
4. If one angle is right, then all angles are right.
5. The diagonals of a parallelogram bisect each other.
6. Each diagonal of a parallelogram separates it into two congruent . Now we can answer our question : Our question is "  How far down (from a vertex) along each diagonal do the diagonals of a parallelogram intersect? ". ANSWER: From a vertex along each diagonal, the diagonal intersects the other diagonal exactly at the middle of the diagonal. If you look to the 5th property given above you will note that our answer to the question is very correct. THANKS