QuadrilateralsTo show ABCD is a parallelogram, it is sufficient to show that:
To show ABCD is a rectangle, it is sufficient to show that it is a parallelogram, and
To show ABCD is a square, it is sufficient to show that it is a rectangle, and
To show ABCD is a rhombus, it is sufficient to show that it is a parallelogram, and
To show ABCD is a kite, it is sufficient to show that there are two pairs of sides with equal magnitudes but are not parallel.
To show ABCD is a trapezium, it is sufficient to show that there is one pair of parallel sides.
TrianglesA circumscribed triangle is
right-angled if one of its side is a diameter.
The others are either dealing with circles or lines, which tend to be quite basic (or not applicable). They're all in my bound reference (somewhere in this board if you look hard enough) if you want them.