UPSKILL MATH PLUS
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Learn moreProve that a parallelogram that can be circumscribed about a circle is a rectangle.
Proof:
Given that, \(WXYZ\) is a cyclic parallelogram.
Therefore, \(∠W+∠Y=\)\(^°\) []
\(∠W=∠\) []
Therefore, \(∠W=∠Y=\)\(=\)\(^°\)
Similarly, \(∠X+∠Z=\)\(^\circ\)
\(∠X=∠\) []
\(∠X=∠Z =\)\(=\)\(^°\) [opposite of a parallelogram]
Each angle of \(WXYZ\) is \(90^°\)
Since, opposite sides are parallel and all the angles are \(90^\circ\), \(WXYZ\) is a rectangle.
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