In the following figures $, ABCD$ is a parallelogram.
find the values of $x$ and $y.$
View full solution →find the values of $x$ and $y.$
Question types
Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] question types
67 questions across 5 question groups — pick any mix to generate a MATHEMATICS paper with step-by-step answer keys.
67
Questions
5
Question groups
5
Question types
01
[2 Mark Question Answer]
9 Q→02[3 marks sum]
6 Q→03[4 marks sum]
25 Q→04[5 marks sum]
17 Q→05TRUE / FALSE
10 Q→Sample Questions
Rectilinear Figures [Quadrilaterals Parallelogram, Rectangle, Rhombus, Square and Trapezium] questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
In the figure, given below, $AM$ bisects angle $A$ and $DM$ bisects angle $D$ of parallelogram $ABCD.$ Prove that: $\angle A D=90^{\circ}$.
View full solution →In a pentagon $ABCDE, AB$ is parallel to $DC$ and $\angle A: \angle E : \angle D = 3: 4: 5.$ Find angle $E$.
View full solution →Two angles of an eight $-$ sided polygon are $142^{\circ}$ and $176^{\circ}.$ If the remaining angles are equal to each other$;$ find the magnitude of each of the equal angles.
View full solution →Three angles of a seven $-$ sided polygon are $132^o$ each and the remaining four angles are equal. Find the value of each equal angle.
View full solution →In the following figure, $\text{ABCD}$ and $\text{PQRS}$ are two parallelograms such that $\angle D =120^{\circ}$ and $\angle Q =70^{\circ}$.Find the value of $x$.
View full solution →The angles of a quadrilateral are in the ratio $3: 4: 5: 6$. Show that the quadrilateral is a trapezium.
View full solution →In parallelogram $\text{ABCD}, AP$ and $AQ$ are perpendiculars from the vertex of obtuse angle $A$ as shown.
If $\angle x : \angle y = 2 : 1$.
find angles of the parallelogram.
View full solution →If $\angle x : \angle y = 2 : 1$.
find angles of the parallelogram.
The ratio between an exterior angle and an interior angle of a regular polygon is $2 : 3.$ Find the number of sides in the polygon.
View full solution →$AB, BC,$ and $CD$ are the three consecutive sides of a regular polygon. If $\text{BAC }= 15^\circ ;$
find,
$(i)$ Each interior angle of the polygon.
$(ii)$ Each exterior angle of the polygon.
$(iii)$The number of sides of the polygon.
View full solution →find,
$(i)$ Each interior angle of the polygon.
$(ii)$ Each exterior angle of the polygon.
$(iii)$The number of sides of the polygon.
The alongside figure shows a parallelogram $\text{ABCD}$ in which $A E=E F$ $= FC$.
Prove that:$(i) DE$ is parallel to $FB(ii) DE = FB(iii) \text{DEBF}$ is a parallelogram.
View full solution →Prove that:$(i) DE$ is parallel to $FB(ii) DE = FB(iii) \text{DEBF}$ is a parallelogram.
$E$ is the mid$-$point of side $AB$ and $F$ is the mid$-$point of side $DC$ of parallelogram $\text{ABCD}$. Prove that $\text{AEFD}$ is a parallelogram.
View full solution →The diagonals of a rectangle intersect each other at right angles. Prove that the rectangle is a square.
In case of a parallelogram.prove that$:(i)$ The bisectors of any two adjacent angles intersect at $90^o.(ii)$The bisectors of the opposite angles are parallel to each other.
View full solution →In the following figure, $\text{ABCD}$ is a parallelogram.
Prove that:$(i) AP$ bisects $\angle A,(ii) B P$ bisects $\angle B,(iii) \angle DAP +\angle BCP =\angle APB$
View full solution →Prove that:$(i) AP$ bisects $\angle A,(ii) B P$ bisects $\angle B,(iii) \angle DAP +\angle BCP =\angle APB$
In parallelogram $\text{ABCD}$, the bisector of $\angle A$ meets $DC$ at $P$ and $AB = 2 AD$.Prove that:$(i) BP$ bisects angle $B.(ii)$ \Angle APB = 90^o$.
View full solution →Prove that the bisectors of the interior angles of a rectangle form a square.
Prove that the bisectors of interior angles of a parallelogram form a rectangle.
Prove that the bisectors of opposite angles of a parallelogram are parallel.
In the given figure, $A B C D$ is a parallelogram. Prove that: $A B=2 B C$.
View full solution →State, $'$true$'$ or $'$false$'$,If the diagonals of a quadrilateral bisect each other at right angle, the quadrilateral is a square.
View full solution →- True
- False
State$, '$true$'$ or $'$false$'$
If two adjacent sides of a parallelogram are equal, it is a rhombus.
View full solution →If two adjacent sides of a parallelogram are equal, it is a rhombus.
- True
- False
State$, '$true$'$ or $'$false$'$,Diagonals of a rhombus are equal.
View full solution →- True
- False
State$, '$true$'$ or $'$false$',$Every parallelogram is a rhombus.
View full solution →- True
- False
State$, '$true$'$ or $'$false$',$Every rhombus is a parallelogram.
View full solution →- True,
- False
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