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!

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  1. 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.

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

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