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Exploring kites
STUDYING DIAGONALS OF KITES
You will need to open the widget, Exploring kites, to do these HOTsheet tasks.
TASK 1
Drag the vertices
a
By dragging the vertices, create as many different kinds
of kites as possible.
b
Select
and create a kite with the side lengths
matching this diagram.
c
Select
diagram.
TASK 2
and fill in all the angle sizes on this
Explore the angles formed by the diagonals of a kite
Create as many kites as you can and find the answers to the questions.
a
Does the diagonal always bisect the vertices between equal sides?
yes/no
b
Does the diagonal always bisect the vertices between unequal sides?
yes/no
c
What is the size of the angle where the two diagonals meet? ______
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 a kite be equal in length? yes/no
b
From your observations, which of the following statements is true?
Both diagonals of a kite bisect each other (cut each other in half).
One diagonal of a kite is bisected (cut in half) by the other.
© 2007 HOTmaths
1
Topic: Exploring Geometry
Exploring kites
TASK 4
Summarise your findings
Tick the statements that are true for all kites.
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)
At least one diagonal bisects the angles of
the quadrilateral
Two pairs of adjacent sides equal
All sides equal
Both diagonals bisect the angles of the
quadrilateral
Adjacent sides perpendicular
At least one pair of opposite angles equal
Both pairs of opposite sides equal
TASK 5
Transform the kite into other shapes
Drag the vertices of the kite to see if you can form other quadrilaterals.
a
A rhombus has all sides equal in length.
Can you form a rhombus from a kite? yes/no
b
A square has all its sides equal in length and all its angles right angles.
Can you form a square from a kite? yes/no
c
A rectangle that is not a square has adjacent sides not equal in length.
Can you form a rectangle that is not also a square from a kite? yes/no
d
Can you form a parallelogram that is not also a rhombus from a kite? yes/no
© 2007 HOTmaths
2
Topic: Exploring Geometry