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A parallelogram is a _________ if and only if its diagonals are congruent.
square.
Thanks!
In order to answer this question, let's first understand what a parallelogram is and what it means for its diagonals to be congruent. Then we can determine the missing word in the given statement.
A parallelogram is a quadrilateral with opposite sides that are both parallel and equal in length. Its opposite angles are also congruent. This means that if you start at one corner of the parallelogram and follow it around, you will encounter two pairs of parallel sides.
Now, let's consider the diagonals of a parallelogram. A diagonal of a parallelogram is a line segment that connects any two non-adjacent vertices of the parallelogram. Since a parallelogram has pairs of parallel sides, its diagonals will intersect at their midpoint.
To say that the diagonals of a parallelogram are congruent means that the two diagonals have the same length. In other words, their lengths are equal.
So, to complete the statement, a parallelogram is a "rhombus" if and only if its diagonals are congruent. A rhombus is a special type of parallelogram where all four sides are congruent. Therefore, if the diagonals of a parallelogram are congruent, then it is a rhombus. Similarly, if a parallelogram is a rhombus, then its diagonals will be congruent.
In summary, the missing word in the given statement is "rhombus".