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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.
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.
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.
Draw a parallelogram and cut it out. Then cut from one corner to the other. You should end up with two triangles.
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Diagonals bisect each other at what angels for a rhombus?
They bisect each other at an angle of 90 degrees
Does a square bisect each other?
The diagonals of any rhombus bisect each other. A square is a special kind of a rhombus.
Do the diagonals of a rectangle bisect each other?
Yes
Does the diagonal of a rectangle bisect each other?
Yes. The diagonals of any parallelogram bisect each other. A rectangle is a special case of a parallelogram.
In parallelogram the diagonals have the same midpoint?
Yes the diagonals of a parallelogram have the same midpoint since they bisect each other.
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.
Do diagonals of a rectangle bisect each other?
The diagonals of a square (which always bisect each other) are the same length.
