answersLogoWhite

0


Best Answer

I can't offer a full proof, but I can suggest some possibilities that will lead you to your proof. In a parallelogram, you can easily demonstrate that the angles formed by a cord extending between parallel lines and the parallel lines themselves, and that are formed on opposite sides of the cord, are equal. This will work for both pairs of triangles in the parallelogram, and can be applied to all of the angles at the corners of the parallelogram. This will lead you to demonstrating that the pairs of triangles "pointing" to each other (not adjacent pairs) are similar, and in fact congruent. From there it is not difficult to establish that the connected sections of the two interior cords are equal.

User Avatar

Wiki User

16y ago
This answer is:
User Avatar
More answers
User Avatar

Wiki User

15y ago

Draw parallelogram ABCD and their diagonals AC and BD intersecting at point E.

Because ABCD is a parallelogram, opposite sides AB and CD are parallel and equal.

Because AB and CD are parallel, angles BDC and ABD are equal. For the same reason, angles ACD and BAC are equal.

Given: AB = CD, angles BDC = ABD and angles ACD and BAC are equal, triangles ABE and CDE are congruent.

Because triangles ABE and CDE are congruent, AE = CE and BE = DE. QED.

This answer is:
User Avatar

User Avatar

Wiki User

8y ago

The statement cannot be proved because it is not true.

As a counter example, consider a parallelogram which is not a rhombus. Its diagonals do bisect each other but, by definition, it is not a rhombus.

This answer is:
User Avatar

User Avatar

Wiki User

13y ago

No, they would make an X shape instead of + shape

This answer is:
User Avatar

User Avatar

Wiki User

11y ago

Draw a parallelogram and cut it out. Then cut from one corner to the other. You should end up with two triangles.

This answer is:
User Avatar

User Avatar

Wiki User

8y ago

You cannot since, in general, the statement is not true.

This answer is:
User Avatar

User Avatar

Wiki User

10y ago

Yes, they do.

This answer is:
User Avatar

User Avatar

Wiki User

12y ago

yes

This answer is:
User Avatar

User Avatar

Wiki User

11y ago

yes they do

This answer is:
User Avatar

Add your answer:

Earn +20 pts
Q: Do a parallelograms diagonals bisect each other?
Write your answer...
Submit
Still have questions?
magnify glass
imp
Related questions

Do all the diagonals of parallelograms bisect each other?

Yes


Which kinds of quadrilaterals have diagonals that bisect each other?

Parallelograms.


What quadrilaterals have diagonals that bisect?

A square has two diagonals that bisect each other at 90 degrees


Do all parallelograms have diagonals which bisect?

Yes; all parallelograms have diagonals that bisect each other. Other properties of parallelograms are: * The opposite sides are congruent. * The opposite sides are parallel. * The opposite angles are congruent.


Does a parallelogram have diagonals that bisect each other?

They do in some parallelograms, not in others.


What quadrilaterals bisect each other?

Quadrilaterals do not bisect each other. They could in special cases. In parallelograms (types of quadrilaterals), the diagonals bisect each other.


Do the diagonals of parallelogram bisect each other?

Yes. Other things about parallelograms: -opposite sides are equal in length. -opposite angles are equal in length. -diagonals bisect each other.


Do parallelograms always bisect each other?

Parallelograms do not normally bisect each other.


Name the best classification for a parallelogram with 4 right angles and diagonals that bisect each other?

A square. All squares are parallelograms, but not all parallelograms are squares.


Why do diagonals on a kite bisect each other?

name 4 diagonals that bisect each other


Do the diagonals of a parrallelogram bisect each other?

Yes, the diagonals of a parallelogram bisect each other.


What is meant by diagonals bisect each other?

By bisecting , we mean cutting into half. So , when the diagonals bisect each other , they then are actually dividing each other into two equal halves. For example , like in quadilaterals , (perhaps parallelograms) , like square,rectangle,rhombus , etc.