0
If you look ate the parallelogram you'll see two kinds of triangles. Two that have longer diagonal and bigger angle, and two sides of parallelogram. Then, you have two triangles that have two sides of parallelogram, shorter diagonal and smaller angle. This triangles obviously have two sides that are the same (sides of parallelogram). If this two triangles had been congruent diagonals would have been congruent too, since these triangles would have been congruent. But this is not true unless angles of parallelogram are the same, therefore diagonals cannot be the same length. Of course, there are parallelograms that have same angles, and those are square and rectangle, which do have the same angles. I hope I made this more clear, and I'm sorry for my bad English.
Add your answer:
Earn +20 pts
Should the diagonals of a parallelogram always be congruent?
No. The diagonals of a parallelogram are congruent if and only if the parallelogram is a rectangle.
Are the diagonals congruent if a rhombus is a parallelogram?
No not normally only if the parallelogram is in the form of a rectangle will it then have congruent diagonals.
The diagonals are congruent but the quadrilateral has no right angles is it a parallelogram?
It can also be a kite. That has two congruent pairs of sides but unlike a parallelogram they are adjacent, not opposite. A parallelogram with congruent diagonals is a rectangle.
What are Parallelogram Are The Diagonals Congruent?
If the diagonals are cong. then the figure is a rectangle.
What is the house builder's theorem?
If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.
The diagonals of a parallelogram are congruent?
No, the diagonals of a parallelogram are not normally congruent unless the parallelogram is a rectangle.
Should the diagonals of a parallelogram always be congruent?
No. The diagonals of a parallelogram are congruent if and only if the parallelogram is a rectangle.
In any parallelogram are the diagonals congruent?
The diagonals are not congruent unless the parallelogram happens to be a rectangle.
In which parallelogram are the diagonals congruent?
If a parallelogram is in the form of a rectangle then both diagonals are congruent in lengths.
Are the diagonals congruent if a rhombus is a parallelogram?
No not normally only if the parallelogram is in the form of a rectangle will it then have congruent diagonals.
Are diagonals of a parallelogram not congruent?
yes. they are not congruent
Can a quadrilateral be a parallelogram is the diagonals are congruent but the quadrilateral has no right angles?
No. If the diagonals of a parallelogram are congruent then it must be a rectangle (or square).
The diagonals are congruent but the quadrilateral has no right angles is it a parallelogram?
It can also be a kite. That has two congruent pairs of sides but unlike a parallelogram they are adjacent, not opposite. A parallelogram with congruent diagonals is a rectangle.
If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle?
true.
A parallelogram has congruent diagonals?
yes
What are Parallelogram Are The Diagonals Congruent?
If the diagonals are cong. then the figure is a rectangle.
The diagonals of a parallelogram must be what?
The diagonals of a parallelogram are congruent (equal in length) and bisect each other.
