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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.
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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.
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.
Does the diagonals of a parallelogram bisect the angles?
No, the diagonals of a parallelogram do not necessarily bisect the angles. The diagonals of a parallelogram divide it into four congruent triangles, but they do not necessarily bisect the angles of those triangles.
