![]() Prove that a cyclic parallelogram is a rectangle.Prove that $ar(\triangle ADF) = ar(\triangle ECF)$. Prove that (i) ar (ABCD) ar (EFCD) Given that ABCD is a. $ABCD$ is a parallelogram in which $BC$ is produced to $E$ such that $CE = BC. Example 1 In given figure, ABCD is a parallelogram and EFCD is a rectangle. ![]() $ABCD$ is a parallelogram, $AD$ is produced to $E$ so that $DE = DC = AD$ and $EC$ produced meets $AB$ produced in $F$.If $P$ is any point on $BO$, prove that $ar(\triangle ABP) = ar(\triangle CBP)$. Show that the line segments AF and EC trisect the diagonal BD. $ABCD$ is a parallelogram whose diagonals intersect at $O$. Ex 8.2, 5 In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively.Since, the opposite sides are equal, side AB is equal to side DC. If $P$ is any point on $BO$, prove that $ar(\triangle ADO) = ar(\triangle CDO)$. The given parallelogram ABCD has the length of AB measures as 9x + 14, and the length of DC measures as 3x + 4 inches. $ABCD$ is a parallelogram whose diagonals intersect at $O$. Given: ABCD is a parallelogram.Prove: A and D are supplementary.By the definition of a parallelogram, ABDC.$E$ is a point on the side $AD$ produced of a parallelogram $ABCD$ and $BE$ intersects $CD$ at $F$.If the area of $\triangle DFB = 3\ cm^2$, find the area of parallelogram $ABCD$. If altitude EF is 16 cm long, find the altitude of the parallelogram to the base AB of. $ABCD$ is a parallelogram in which $BC$ is produced to $E$ such that $CE = BC. 9.32, area of AFB is equal to the area of parallelogram ABCD.The sides $AB$ and $CD$ of a parallelogram $ABCD$ are bisected at $E$ and $F$.If $P$ is any point in the interior of a parallelogram $ABCD$, then prove that area of the triangle $APB$ is less than half the area of parallelogram.$ABCD$ is a parallelogram, $G$ is the point on $AB$ such that $AG = 2GB, E$ is a point of $DC$ such that $CE = 2DE$ and $F$ is the point of $BC$ such that $BF = 2FC$.Find what portion of the area of parallelogram is the area of $\triangle EFG$.
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