$\text{ABCD}$ is a parallelogram. The bisector of $\angle BAD$ meets $\text{DC}$ at $P,$ and $\text{AD}$ is half of $\text{AB}.$
Prove that$: \text{BP}$ bisects $\angle ABC.$
View full solution →Prove that$: \text{BP}$ bisects $\angle ABC.$
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Quadrilaterals question types
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Sample Questions
Quadrilaterals questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
$\text{ABCD}$ is a parallelogram. $P$ and $Q$ are mid$-$points of $\text{AB}$ and $\text{CD}.$ Prove that $\text{APCQ}$ is also a parallelogram.
View full solution →$\text{ABCD}$ is a rectangle with $\angle ADB = 55^\circ ,$ calculate $\angle ABD.$
View full solution →$\text{ABCD}$ is a parallelogram. The bisector of $\angle BAD$ meets $DC$ at $P,$ and $AD$ is half of $AB.$
Prove that: $\angle APB$ is a right angle.
View full solution →Prove that: $\angle APB$ is a right angle.
$\text{PQRS}$ is a parallelogram. $T$ is the mid$-$point of $PQ$ and $ST$ bisects $\angle PSR.$
Prove that: $RT$ bisects angle $R$
View full solution →Prove that: $RT$ bisects angle $R$
$\text{PQRS}$ is a parallelogram. $PQ$ is produced to $T$ so that $PQ = QT.$ Prove that $PQ = QT$. Prove that $ST$ bisects $QR$.
View full solution →$\text{ABCD}$ is a parallelogram. $P$ and $T$ are points on $AB$ and $DC$ respectively and $AP = CT.$ Prove that $PT$ and $BD$ bisect each other.
View full solution →$\text{PQRS}$ is a parallelogram. $T$ is the mid$-$point of $R S$ and $M$ is a point on the diagonal $P R$ such that $M R=\frac{1}{4} PR. TM$ is joined and extended to cut $QR$ at $N$. Prove that $QN = RN$.
View full solution →Prove that if the diagonals of a parallelogram are equal then it is a rectangle.
In a parallelogram $\text{ABCD}, E$ is the midpoint of $AB$ and $DE$ bisects angle $D$. Prove that:$CE$ is the bisector of $\angle C$ and $\angle DEC$ is a right angle.
View full solution →In a parallelogram $\text{ABCD}, E$ is the midpoint of $AB$ and $DE$ bisects $\angle D$. Prove that: $BC = BE.$
View full solution →In the given figure,$\text{PQRS}$ is a parallelogram in which $PA = AB$ Prove that: $\text{SAQB}$ is a parallelogram.
View full solution →Prove that the quadrilateral formed by joining the mid$-$points of consecutive sides of a rhombus is a rectangle.
View full solution →Prove that the quadrilateral formed by joining the mid$-$points of consecutive sides of a rectangle is a rhombus.
View full solution →$\text{ABCD}$ is a quadrilateral $P, Q, R$ and $S$ are the mid$-$points of $AB, BC, CD$ and $AD$. Prove that $\text{PQRS}$ is a parallelogram.
View full solution →The diagonals $PR$ and $QS$ of a quadrilateral $\text{PQRS}$ are perpendicular to each other.$ A, B, C$ and $D$ are mid$-$point of $PQ, QR, RS$ and $SP$ respectively. Prove that $\text{ABCD}$ is a rectangle.
View full solution →Prove that the quadrilateral formed by joining the mid$-$points of a square is also a square.
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