easiest question?

Question

decide if these statement are true , sometime true or never

1 . a polygon with equal sides is regular
2 . a parallelogram is a rhombus
3. a parallelogram is a trapezoid

Answer 1

1. Sometimes true, as we can have bent hexagons with equal sides
2. Sometimes true, as parallelograms don't always have equal sides
3. False, as both pairs of sides of a trapezoid are generally not parallel, otherwise it'd be called a rectangle or parallelogram

The trouble with 3 is that there isn't an agreed definition of "trapezoid", because some authors say that it means "any" shape with at least 2 sides that are parallel, so that sometimes 3 can be true. But others say "exactly one pair of sides" are parallel, in which case 3 is false. See wiki on this.

Answer 2

1. sometimes; you also need every angle to be equal, which is not always the case

2. sometimes; a parallelogram need not have all sides equal. It's pairs of opposite sides must be equal to each other, but not necessarily to the other pair (if that makes sense). Note however that a rhombus is always a parallelogram.

3. always; a trapezoid has at least one pair of parallel sides. Note however that sometimes a trapezoid is defined to have exactly one pair of parallel sides, in which case this would be never.