How does the area of the parallelogram you get by connecting the midpoints of the quadrilateral relate to the original quadrilateral?

How does the area of the parallelogram you get by connecting the midpoints of the quadrilateral relate to the original quadrilateral?

The midpoints of the sides of an arbitrary quadrilateral form a parallelogram. If the quadrilateral is convex or concave (not complex), then the area of the parallelogram is half the area of the quadrilateral. The theorem can be generalized to the midpoint polygon of an arbitrary polygon.

Why do connecting the midpoints of a quadrilateral form a parallelogram?

Logically that means the diagonals midpoints must be the same. Since the midpoints of the diagonals are the same, the diagonals bisect each other. Therefore, they are the diagonals of a parallelogram. Shown in the middle figure.

When the midpoints of the sides of a quadrilateral are connected the new quadrilateral is a parallelogram?

If you connect the midpoints of the sides of any quadrilateral, the resulting quadrilateral is always a parallelogram. Surprisingly, this is true whether it is a special kind of quadrilateral like a parallelogram or kite or trapezoid, or just any arbitrary simple convex quadrilateral with no parallel or equal sides.

Is midpoint parallelogram equal?

If you connect mid-point to mid-point of sides of the original parallelogram you will have another parallelogram, where opposite sides of this new parallelogram are both parallel and equal, and the included angles are right angles.

What does the midpoint formula prove?

The midpoint M is then defined by M = ((x + X)/2,(y + Y)/2). To show that M is really the midpoint of the line segment PQ, we need to show that the distance between M and Q is the same as the distance between M and P and that this distance is half the distance from P to Q.

How do you prove a parallelogram?

There are five ways to prove that a quadrilateral is a parallelogram:

1. Prove that both pairs of opposite sides are congruent.
2. Prove that both pairs of opposite sides are parallel.
3. Prove that one pair of opposite sides is both congruent and parallel.
4. Prove that the diagonals of the quadrilateral bisect each other.

How do you prove Varignons theorem?

Varignon’s Theorem: Moment of a force about any point is equal to the sum of the moments of the components of that force about the same point. which says that the moment of R about O equals the sum of the moments about O of its components P and Q . This proves the theorem.

How do you prove Varignons Theorem?

How do you prove a parallelogram is vector?

Answer: Let A, B, C, D be the four sides; then if the vectors are oriented as shown in the figure below we have A + B = C + D. Thus two opposite sides are equal and parallel, which shows the figure is a parallelogram.

How do you prove a quadrilateral is a parallelogram?

The only shape you can make is a parallelogram. If both pairs of opposite angles of a quadrilateral are congruent, then it’s a parallelogram (converse of a property). If the diagonals of a quadrilateral bisect each other, then it’s a parallelogram (converse of a property).

How do you know if a quadrilateral is always a parallelogram?

If you connect the midpoints of the sides of any quadrilateral, the resulting quadrilateral is always a parallelogram. Surprisingly, this is true whether it is a special kind of quadrilateral like a parallelogram or kite or trapezoid, or just any arbitrary simple convex quadrilateral with no parallel or equal sides.

How do you make a parallelogram from midpoints?

Parallelogram Formed by Connecting the Midpoints of a Quadrilateral 1 Problem. In a quadrilateral ABCD, the points P, Q, R and S are the midpoints of sides AB, BC, CD and DA, respectively. 2 Strategy. The fact that we are told that P, Q, R and S are the midpoints should remind us of the Triangle Midsegment… 3 Proof. More

How do you make a quadrilateral have opposite sides parallel?

When we connect the midpoints (the point exactly half-way along a line) of each side of the quadrilateral, one after the other, we create a new shape that has opposite sides parallel, even though the containing quadrilateral might not. To see why, click on the “Diags” button and drag the points around, while thinking “midpoints”.

What is the midpoint of a quadrilateral ABCD?

In quadrilateral ABCD points P, Q, R, S are midpoints of side AB, BC, CD and AD respectively. Draw diagonal BD. As PS is the midsegment of ▲ ABD, we can say that PS || BD. As QR is the midsegment of ▲ BCD, we can say that QR || BD.