Kites Up Close
The diagonals of a kite are perpendicular,
but that’s not all there is to say about them.
For starters, one diagonal bisects the other,
meaning it chops the other diagonal in half.
It also bisects the pair of opposite angles, and
if you look at the remaining pair of angles,
they’re congruent, too. So there’s a lot you
can know about a kite without having to do
Area and perimeter
As you discovered earlier, you find the area of a kite by
multiplying together the lengths of the two diagonals and
dividing by two. To find the perimeter, remember that
there are two pairs of congruent sides so you only have to
add the two different sides together and multiply by two.
the other diagonal.
these angles, too.
hese angles ar
So the diagonals of a kite
are perpendicular. What about the
diagonals of a parallelogram, are they
A:In general, parallelograms don’t have
The diagonals of a parallelogram are
still important though. If a shape is a
parallelogram, then its diagonals bisect
each other. Try adding diagonals to the
parallelograms earlier in the chapter and
you’ll see what we mean.
Could I have calculated the area
of the kite by splitting it into simpler
shapes like before?
A:You could, but it would have taken
you much longer to calculate. All you really
need to do is multiply the two diagonals
together and divide the result by 2.
The kites we’ve looked at in this
chapter look symmetrical. Is that a
A:No, not at all. Every kite is
symmetrical along one diagonal.
Can a shape be both a
parallelogram and a kite?
A:Yes it can. A shape is a parallelogram
and a kite if it fits the description of both.
In other words, it must have two pairs of
separate adjacent congruent sides, and
also the opposing sides must be parallel.
This means that all four sides must be
An example of a shape that is both a
parallelogram and a kite is a square. All four
sides are congruent, and opposite sides are
parallel. We’ll get to that in a little bit.…
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