Andhra Pradesh Board Solutions for Chapter: Quadrilaterals, Exercise 5: EXERCISE - 8.3

$ABCD$ is a parallelogram $AP$ and $CQ$ are perpendiculars drawn from vertices $A$ and $C$ on diagonal $BD$, show that $∆APB\cong ∆CQD$

$ABCD$ is a parallelogram $AP$ and $CQ$ are perpendiculars drawn from vertices $A$ and $C$ on diagonal $BD$, show that $AP=CQ$

In $∆ABC$ and $∆DEF$, $AB=DC$ and $AB\parallel DE$; $BC=EF$ and $BC\parallel EF$. Vertices $A, B$ and $C$ are joined to vertices $D, E$ and $F$ respectively. Show that $ABED$ is a parallelogram.

In $∆ABC$ and $∆DEF$, $AB=DC$ and $AB\parallel DE$; $BC=EF$ and $BC\parallel EF$. Vertices $A, B$ and $C$ are joined to vertices $D, E$ and $F$ respectively. Show that $BCFE$ is a parallelogram.

In $∆ABC$ and $∆DEF$, $AB=DC$ and $AB\parallel DE$; $BC=EF$ and $BC\parallel EF$. Vertices $A, B$ and $C$ are joined to vertices $D, E$ and $F$ respectively. Show that $AC=DF$.

In $∆ABC$ and $∆DEF$, $AB=DC$ and $AB\parallel DE$; $BC=EF$ and $BC\parallel EF$. Vertices $A, B$ and $C$ are joined to vertices $D, E$ and $F$ respectively. Show that $∆ABC\cong ∆DEF$.

$ABCD$ is a parallelogram. $AC$ and $BD$ are the diagonals intersect at $O$. $P$ and $Q$ are the points of trisection of the diagonal $BD$. Prove that $CQ\parallel AP$ and also $AC$ bisects $PQ$

$ABCD$ is a square. $E, F, G$ and $H$ are the midpoints of $AB, BC, CD$ and $DA$ respectively. Such that $AE=BF=CG=DH$. Prove that $EFGH$ is a square.