Math Is Fun Forum

mathland

Member

Registered: 2021-03-25

Posts: 444

Parallelogram Proof

Prove that the diagonals of the parallelogram
in the figure intersect at their midpoints.

Here are the 4 points representing the four corners of the
parallelogram:

Point (b, c) across point (a, 0).

Point (0, 0) across point (a + b, c).

Note: Point (0, 0) is the origin on the xy-plane.

I think the distance formula for points is applied here. Yes?

What is the difference between the words prove and proof in mathematics?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Parallelogram Proof

There may be a way using the distance formula but I think the algebra would get complicated because of the squaring involved.

I'll add some letters to your coordinates to make a simpler method clearer.

O (0,0)  A (a,0)  B (a+b,c) C (b,c)

Construct the equations for the lines OB and AC.

Using simultaneous equations find the point M where these lines cross.

Use the midpoint theorem to find the midpoints of OB and also AC.

Show that the midpoints are both at M.

Bob

ps.  Prove is a verb.  So to prove something you have to do something.

Proof is a noun.  It is the noun that gives a name to the 'something' that you did when you proved.

eg.

If 2x + 3 = 7 prove that x = 2.

Proof:  2x + 3 = 7    =>     2x + 3 - 3 = 7 - 3     =>       2x = 4      =>      2x/2 = 4/2       =>   x = 2

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathland

Member

Registered: 2021-03-25

Posts: 444

Re: Parallelogram Proof

There may be a way using the distance formula but I think the algebra would get complicated because of the squaring involved.

I'll add some letters to your coordinates to make a simpler method clearer.

O (0,0)  A (a,0)  B (a+b,c) C (b,c)

Construct the equations for the lines OB and AC.

Using simultaneous equations find the point M where these lines cross.

Use the midpoint theorem to find the midpoints of OB and also AC.

Show that the midpoints are both at M.

Bob

ps.  Prove is a verb.  So to prove something you have to do something.

Proof is a noun.  It is the noun that gives a name to the 'something' that you did when you proved.

eg.

If 2x + 3 = 7 prove that x = 2.

Proof:  2x + 3 = 7    =>     2x + 3 - 3 = 7 - 3     =>       2x = 4      =>      2x/2 = 4/2       =>   x = 2

Very good. I'll work on it.