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Exploring kites
SOLUTIONS
STUDYING DIAGONALS OF KITES
TASK 1
c
Drag the vertices
Your angles should be the same as these or very similar.
TASK 2
Explore the angles formed by the diagonals of a kite
a
Does the diagonal always bisect the vertices between equal sides?
yes
b
Does the diagonal always bisect the vertices between unequal sides?
no
c
What is the size of the angle where the two diagonals meet?
90º
TASK 3
Explore lengths of the diagonals of a kite
Select
then drag a vertex and watch the lengths of the diagonals change.
a
Must the two diagonals of kites be equal in length? no
b
The second statement is correct: One diagonal of a kite is bisected (cut in half) by the other.
TASK 4
Summarise your findings
At least one pair of opposite sides parallel
Diagonals equal in length
Two pairs of opposite sides parallel
At least one diagonal bisects the other
Two pairs of opposite sides equal
Both diagonals bisect each other
Diagonals are perpendicular (intersect at right angles)

All sides equal
At least one diagonal bisects the angles of the quadrilateral

Adjacent sides perpendicular
Both diagonals bisect the angles of the quadrilateral
Two pairs of adjacent sides equal
At least one pair of opposite angles equal



Both pairs of opposite sides equal
TASK 5
Transform the kite into other shapes
a
Can you form a rhombus from a kite? yes So a rhombus is special example of a kite.
b
Can you form a square from a kite? yes So a square is special example of a kite.
c
Can you form a rectangle that is not also a square from a kite? no So a rectangle is not a special
example of a kite.
d
Can you form a parallelogram that is not also a rhombus from a kite? no So a parallelogram is not
a special example of a kite.
© 2007 HOTmaths
Topic: Exploring Geometry