a.)If ABCD is a parallelogram, then ABCD is (always true, sometimes true, OR never true) a rectangle.

b.)The diagonals of a square (always true, sometimes true, OR never true) bisect each other.
c.)If WXYZ is a rectangle, then the diagonals are (always true, sometimes true, OR never true) congruent.
d.)The diagonals of a rectangle are (always true, soemtimes true, OR never true) perpendicular.

Please answer each of these with either always true, sometimes true, or never true. If you can provide examples and explanations for the answers you get, do so please!
Thanks!

A) Sometimes

- Parallelogram has sides that parallel to each other. Therefore this can be a rhombus, square or rectangle.
B) Always
-Sides of a square are all equal. All the angles are right. If you draw 1 diagonal you get a right triangle. A^2+B^2=C^2. This will be the same for the other diagonal as well. Because all the sides are equal so will the diagonals.
C) Always
-Similar consept as part (b).
D) Always
-Can't explain this one sorry. It was just a rule in our Geometry class.

a) Sometimes true.

A parallelogram can be a rectangle if its angles are all right angles. However, a parallelogram can also be a rhombus or a square, which do not necessarily have right angles.

b) Always true.
In a square, the diagonals bisect each other. This can be observed by drawing a square and extending the diagonals to meet at their midpoints.

c) Sometimes true.
In a rectangle, the diagonals are always congruent. However, in other quadrilaterals like squares and rhombuses, the diagonals can also be congruent.

d) Always true.
The diagonals of a rectangle are always perpendicular. This can be proven by using the properties of rectangles, which state that opposite sides are parallel and adjacent sides are perpendicular. By drawing a rectangle and measuring the angles formed by the diagonals, it can be observed that they are always 90 degrees.

a.) If ABCD is a parallelogram, then ABCD is (always true, sometimes true, OR never true) a rectangle.

The answer is sometimes true.
Explanation: A parallelogram can have different shapes and sizes, but a rectangle is a specific type of parallelogram. All rectangles are parallelograms, but not all parallelograms are rectangles. For example, the parallelogram ABCD below is not a rectangle.

A_____________B
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D_____________C

b.) The diagonals of a square (always true, sometimes true, OR never true) bisect each other.
The answer is always true.
Explanation: In a square, the diagonals always bisect each other into two congruent segments. For example, in the square below, the diagonal AC bisects the diagonal BD.

A_____________B
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D_____________C

c.) If WXYZ is a rectangle, then the diagonals are (always true, sometimes true, OR never true) congruent.
The answer is always true.
Explanation: In a rectangle, the diagonals are always congruent to each other. For example, in the rectangle below, the diagonal AC is congruent to the diagonal BD.

A_____________B
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D_____________C

d.) The diagonals of a rectangle are (always true, sometimes true, OR never true) perpendicular.
The answer is always true.
Explanation: In a rectangle, the diagonals are always perpendicular to each other. For example, in the rectangle below, the diagonal AC is perpendicular to the diagonal BD.

A_____________B
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D_____________C

D)Sometimes. Only if a rectangle is a square.