Which of the following statements are true? (A) If a kite is also a parallelogram, then it must be a rhombus. (B) If a trapezoid is also a parallelogram, then

Incorrect

Apperently, A and C are wrong.

C alone is wrong too.

Here is one problem with this question.

According to several sources on the net a trapexium is the same thing as a trapezoid BUT

according to Wolfram|Alpha, and I quote

"There are two common definitions of the trapezium. The American definition is a quadrilateral with no parallel sides; the British (AND AUSTRALIAN)  definition is a quadrilateral with two sides parallel (e.g., Bronshtein and Semendyayev 1977, p. 174)--which Americans call a trapezoid."

So before all these answers can be accepted or rejected we may have to agree upon a defintion of a trapezium or trapezoid!

However, A is still definitely correct  :)

I suppose I should at least give reasons

(A) If a kite is also a parallelogram, then it must be a rhombus.

With Kites and rhombuses the diagonals MUST intersect at right angles.

Parallelograms have opposite sides parallel.

A parallelogram where the diagonals interect at right angles is a rhombus

So A is DEFINITELY correct

(B) If a trapezoid is also a parallelogram, then it must be a rhombus.

All parallelograms are trapeziums (they have at least one pair of parallel sides)

so If a trapezoid is also a parallelogram it can be ANY parallelogram

so B is false

(C) If a trapezoid is also a kite, then it must be a parallelogram.

This one depends on the definition of a trapezoid.  Using the American definition it is definitely false.

Using the English (and Australia) definition it is true but it is harder to prove.

(D) If a rhombus is also a trapezoid, then it must be a kite.

All rhombuses are trapeziums. end of story. false