Question

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Answer 1

Notice that in 1.), the diagonal AC is divided in to 2 halves. One half is 3x and the other half is 4x - 5. We know that both halves must be the same length hence 3x and 4x-5 must also be equal. So let's equate 2x and 4x-5 since we know they must be equal and solve for x:\[\bf 3x=4x-5 \implies x = 5\]So for a value of x = 5, ABCD in 1.) will be a parallelogram.

The same thinking/technique can be applied to the rest of the questions. @MayMay_69