2.Given two segments with lengths x and y (x does not equal y), which three special parallelograms meet the three sets of given conditions?
a. One diagonal has length x, the other has length y.
b. The diagonals intersect at right angles.
c. Both diagonals have length y and do not intersect at right angles.
The three special parallelograms that meet the given conditions are:
1. Rectangle:
- One diagonal has length x, the other has length y.
- The diagonals intersect at right angles.
- Both diagonals have length y and do not intersect at right angles.
2. Rhombus:
- One diagonal has length x, the other has length y.
- The diagonals intersect at right angles.
- Both diagonals have length y and do not intersect at right angles.
3. Parallelogram:
- One diagonal has length x, the other has length y.
- The diagonals intersect at right angles.
- Both diagonals have length y and do not intersect at right angles.
These are the three special parallelograms that satisfy the given conditions.
To answer this question, let's start by understanding what special parallelograms meet the given conditions.
a. One diagonal has length x, the other has length y:
In this case, the special parallelogram that meets this condition is a rectangle. In a rectangle, the opposite sides are equal in length, and the diagonals bisect each other at 90 degrees.
b. The diagonals intersect at right angles:
When the diagonals of a parallelogram intersect at right angles, it is called a rhombus. In a rhombus, the opposite sides are equal, but the diagonals are different in length.
c. Both diagonals have length y and do not intersect at right angles:
In this case, we have a parallelogram with equal diagonals that are not at right angles. This type of parallelogram is called a kite. In a kite, both pairs of adjacent sides are equal in length, but the diagonals are not equal, and they do not intersect at right angles.
So, based on the given conditions, the three special parallelograms that meet the conditions are a rectangle, a rhombus, and a kite.
If only special parallelograms are considered (i.e. not just any parallelogram), they would be
- rectangle
- rhombus
- square
Note: one of these choices will fit more than one situation.
I will leave it to you to sort out which one is which, and feel free to post your answer for checking.
rhombus is a
rectangle is c
and square is b