The quality of shapes

Question

Look at each statement, and decide whether or not it is always true.

1)The diagonals of a rectangle are the same length
2) The diagonals of a kite are the same length
3)The diagonals of a kite meet at right angles
4)The diagonals of a rectangle meet at right angles
5)If you join together the midpoints of adjacent sides of a quadrilateral you get a rectangle
6) If the diagonals of a quadrilateral meet at their midpoints, then it is a rhombus

 

For each statement, if it is always true, explain why.
If it is not always true, give an example of a situation in which it is false.

Answer 1

1)The diagonals of a rectangle are the same length - always true
2) The diagonals of a kite are the same length - not true, only true when the kit is a diamond
3)The diagonals of a kite meet at right angles - always true
4)The diagonals of a rectangle meet at right angles - not true, only true when the rectangle is a square
5)If you join together the midpoints of adjacent sides of a quadrilateral you get a rectangle - The wording for this statement is not clear to me.  If I have a rectangle and mark the midpoint of each side and draw a line between adjacent midpoints, I would get a triangle, not a rectangle.
6) If the diagonals of a quadrilateral meet at their midpoints, then it is a rhombus - this would also be true of a rectangle or square