Further thoughts on this homework sheet.
I believe it is a requirement of the curriculum that children learn the properties of shapes and the correct names for shapes.
It sounds like this sheet is designed to get children looking at the properties of the shapes on the sheet; identifying those that a set of shapes have in common; and then finding a good 'name', 'description', or 'title' for those shapes.
There is no one correct answer.
Look at my example below. Any of the following is an answer.
Straight sided, closed shapes.
Four sided shapes with at least one pair of parallels.
So if the child puts a suitable title, she has satisfied the homework.
But, to show off how well she has met the curriculum objectives, some answers are better than others.
I wouldn't give high marks for "I called them Henry because that was what they looked like to me." although I'd probably laugh and make a mental note that here is a very clever child.
I would try to avoid using the same Title twice and, if I could see several possibilities I'd try to put them all:
eg. 'Polygons which are quadrilaterals with a pair of parallel sides.'
In fact, the best outcome from the homework has already been satisfied. Parents are taking an interest in their child's school work and showing they think it's important.
It could also be argued that showing that even parents don't always know the answers is beneficial.
Plus, they have discovered Maths Is Fun and that's got to be a good thing!
See http://www.mathsisfun.com/geometry/polygons.html and similar pages for hints.