b) the diagonals of a parallelogram always bisect its angles. --- draw a parallelogram ABCD, angle ABC = CDA, so when you draw a diagonal, it'll bisect
c) a quadrilateral with one pair of congruent sides and one pair of parallel sides is always a parallelogram. --- Draw a quadrilateral ABCD, let AB // DC. For AD to be of the same length (congruent) as BC, they must be inclined at the same angle, otherwise you can never get equal lengths -- you can see this easily by drawing AB and DC to be parallel but of different lengths.
d) the diagonals of a rhombus are sometimes congruent. -- square
e) the consecutive sides of a rectangle are always perpendicular to each other. -- a rectangle abcd, ab is perpendicular to bc is perpendicular to cd is perpendicular to da
h) the diagonals of a parallelogram are sometimes perpendicular bisectors of each other. --rhombus
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I'll be giving +1 rep to everyone real soon, as I already figured out the answers hehe
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