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- Property: The Opposite Angles of a Parallelogram Are of Equal Measure.
- Theorem: If in a Quadrilateral, Each Pair of Opposite Angles is Equal, Then It is a Parallelogram.
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Text
Examples: Sanya has a piece of land which is in the shape of a rhombus (see following Fig). She wants her one daughter and one son to work on the land and produce different crops. She divided the land in two equal parts. If the perimeter of the land is 400 m and one of the diagonals is 160 m, how much area each of them will get for their crops?
Solution : Let ABCD be the field.
Perimeter = 400 m
So, each side = 400 m ÷ 4 = 100 m.
i.e. AB = AD = 100 m.
Let diagonal BD = 160 m.
Then semi-perimeter s of ∆ ABD is given by
`s = (100 + 100 + 160)/2 m = 180 m`
Therefore, area of ∆ ABD
=`sqrt (180 (180 - 100)(180 - 100)(180 - 160))`
`= sqrt (180 * 80 * 80 * 20) m^2 = 4800 m^2`
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