In and
(given rhombus , diagonal bisects )
(s opp equal sides)
similarly
and
but these are alternate interior s
and
is a parallelogram
(opp sides of m)
is a rhombus (all sides equal and two pairs of sides parallel)
We think you are located in South Africa. Is this correct?
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Chapter summary

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Area of a polygon

In and
(given rhombus , diagonal bisects )
(s opp equal sides)
similarly
and
but these are alternate interior s
and
is a parallelogram
(opp sides of m)
is a rhombus (all sides equal and two pairs of sides parallel)
Prove that is a parallelogram.
Prove that is a parallelogram.
(given)
(given)
(Midpt Theorem)
(given)
(given)
(Midpt Theorem)
is a parallelogram (both pairs opp. sides parallel)
Prove that .
(given)
(given)
(Midpt Theorem)
(given)
Prove is the midpoint of .
If and the area of is , calculate the area of .
Prove that the area of will always be four times the area of , let and .
Given quadrilateral with sides and . Also given: and ; and . Complete the proof below to prove that is a parallelogram.
The completed proof looks like this:
Calculate the value of .
is a parallelogram, .
Opposite s of parallelogram are equal. and .
Therefore, .
Calculate the value of .
s in a
Now we know that and that .
.
Study the quadrilateral with opposite angles and angles carefully. Fill in the correct reasons or steps to prove that the quadrilateral is a parallelogram.
Study the quadrilateral with and carefully. Fill in the correct reasons or steps to prove that the quadrilateral is a parallelogram.
In parallelogram , the bisectors of the angles have been constructed, indicated with the red lines below. You are also given , , , , and .
Prove that the quadrilateral is a parallelogram.
Show that is a parallelogram.
Show that is a parallelogram.
But and are diagonals of , is a parallelogram (diagonals bisect each other).
Prove that .
(proved above).
We note that:
We also note that:
Now we can show that is congruent to :
Finally we can show that is a straight line:
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Area of a polygon
