# The sides means of a quadrilateral are the peaks of a parallelogram

Ali the chemical
Visitor
2016-06-02 09:28:27
#1
Let ABCD be a quadrilateral some. Demonstrate that its sides means are the peaks of a parallelogram: a) in the case of convex quadrilateral ABCD. b) if the concave quadrilateral ABCD.

## RE: The sides means of a quadrilateral are the peaks of a parallelogram

TeacherM
Visitor
2016-06-02 10:51:22
#2
We have the figure below, with convex quadrilateral ABCD and M, N, P and Q means its sides. In the figure above we have:

1) M - mid AB

2) N - mid BC

From these two relationships => MN - medium line in ?ABC => MN || MN = AC and AC / 2

In analogy to prove that PQ - middle line in the triangle ADC => PQ || AC and AC = PQ / 2

So we have MN || AC || PQ => MN || PQ

and MN = PQ = AC / 2

As we know, a convex quadrilateral has two opposite sides parallel and congruent is parallelogram => MNPQ - parallelogram

### Forum

Here you can discuss about mathematic, about algebra, geometry, trigonometry.

It is not mandatory to be logged in on this forum but it is nice to have an account. You can ask about mathematics just with your name and your email.

This maths forum is one of the easiest forums to use it.

>> Go to Math Forum 