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question_answer1)
In the parallelogram\[ABCD\], \[AP\] and \[BP\] are bisectors of\[\angle A\]and\[\angle B\]which meet at\[P\].
What is \[2\angle APB\] equivalent to?
A)
\[\angle A+\angle B\] done
clear
B)
\[\angle A+\angle C\] done
clear
C)
\[\angle B+\angle D\] done
clear
D)
\[\angle A-\angle D\] done
clear
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question_answer2)
In the given figure, \[AO\] and \[DO\] are the bisectors of \[\angle A\] and \[\angle D\] of the quadrilateral\[ABCD\]. Find\[\angle AOD\].
A)
\[{{67.5}^{o}}\] done
clear
B)
\[{{77.5}^{o}}\] done
clear
C)
\[{{87.5}^{o}}\] done
clear
D)
\[{{99.75}^{o}}\] done
clear
View Solution play_arrow
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question_answer3)
In a parallelogram find the sum of the bisected angles of two adjacent angles.
A)
\[{{30}^{o}}\] done
clear
B)
\[{{45}^{o}}\] done
clear
C)
\[{{60}^{o}}\] done
clear
D)
\[{{90}^{o}}\] done
clear
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question_answer4)
The diameter of the circumcircle is the diagonal of a rectangle which is \[10\,\,cm\] and breadth of the rectangle is\[6\,\,cm\]. Find its length.
A)
\[6\,\,cm\] done
clear
B)
\[5\,\,cm\] done
clear
C)
\[8\,\,cm\] done
clear
D)
\[7\,\,cm\] done
clear
View Solution play_arrow
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question_answer5)
In the parallelogram\[ABCD\], what are the measures of the angles\[x\]and\[y\]?
A)
\[{{60}^{o}},\,\,{{30}^{o}}\] done
clear
B)
\[{{30}^{o}},\,\,{{60}^{o}}\] done
clear
C)
\[{{45}^{o}},\,\,{{45}^{o}}\] done
clear
D)
\[{{90}^{o}},\,\,{{90}^{o}}\] done
clear
View Solution play_arrow
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question_answer6)
In parallelogram\[PQRS\], what are the values of \[\angle QSP\]and\[\angle SPQ\]?
A)
\[{{45}^{o}},\,\,{{60}^{o}}\] done
clear
B)
\[{{60}^{o}},\,\,{{45}^{o}}\] done
clear
C)
\[{{70}^{o}},\,\,{{35}^{o}}\] done
clear
D)
\[{{35}^{o}},\,\,{{70}^{o}}\] done
clear
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question_answer7)
In the given figure, \[ABCD\] is a trapezium in which\[AB=7\,\,cm,\,\,AD=BC=5\,\,cm\], \[DC=x\,\,cm\] and the distance between \[AB\] and \[DC\] is\[4\,\,cm\]. What is the value of\[x\]?
A)
\[13\,\,cm\] done
clear
B)
\[16\,\,cm\] done
clear
C)
\[19\,\,cm\] done
clear
D)
\[12\,\,cm\] done
clear
View Solution play_arrow
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question_answer8)
In a square\[ABCD\], the diagonals bisect at\[O\]. What type of a triangle is\[\Delta AOB\]?
A)
An equilateral triangle. done
clear
B)
An isosceles but not a right angled triangle. done
clear
C)
A right angled but not an isosceles triangle. done
clear
D)
An isosceles right angled triangle. done
clear
View Solution play_arrow
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question_answer9)
\[ABCD\] is a quadrilateral. If \[AC\] and \[BD\] bisect each other, what is\[ABCD\]?
A)
A square done
clear
B)
A rectangle done
clear
C)
A parallelogram done
clear
D)
A rhombus done
clear
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question_answer10)
In a parallelogram\[ABCD,\]\[\angle D={{60}^{o}}\]. Find the measure of\[\angle A\].
A)
\[{{120}^{o}}\] done
clear
B)
\[{{65}^{o}}\] done
clear
C)
\[{{90}^{o}}\] done
clear
D)
\[{{75}^{o}}\] done
clear
View Solution play_arrow
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question_answer11)
\[ABCD\] and \[MNOP\] are quadrilaterals as shown in the figure.
Which of these is correct?
A)
\[p+q+r+s=w+x+y+z\] done
clear
B)
\[p+q+r+s<w+x+y+z\] done
clear
C)
\[p+q+r+s>w+x+y+z\] done
clear
D)
\[p+q+x+y=r+s+w+z\] done
clear
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question_answer12)
In parallelogram\[ABCD,\] \[AB=12\,\,cm\]. The altitudes corresponding to the sides \[AB\] and \[AD\] are respectively \[9\,\,cm\] and\[11\,\,cm\]. Find\[AD\].
A)
\[\frac{108}{11}cm\] done
clear
B)
\[\frac{108}{10}cm\] done
clear
C)
\[\frac{99}{10}cm\] done
clear
D)
\[\frac{108}{17}cm\] done
clear
View Solution play_arrow
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question_answer13)
In quadrilateral\[ABCD\], if the diagonals \[AC\] and \[BD\] are equal and perpendicular to each other, what is\[ABCD\]?
A)
A square done
clear
B)
A parallelogram done
clear
C)
A rhombus done
clear
D)
A trapezium done
clear
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question_answer14)
One of the diagonals of a rhombus is equal to its side. Find the angles of the rhombus.
A)
\[{{60}^{o}}\]and\[{{80}^{o}}\] done
clear
B)
\[{{60}^{o}}\]and\[{{120}^{o}}\] done
clear
C)
\[{{120}^{o}}\]and\[{{240}^{o}}\] done
clear
D)
\[{{100}^{o}}\]and\[{{120}^{o}}\] done
clear
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question_answer15)
The perimeter of a parallelogram is\[180\,\,cm\]. One side exceeds another by\[10\,\,cm\]. What are the sides of the parallelogram?
A)
\[40\,\,cm\] and\[50\,\,cm\] done
clear
B)
\[45\,\,cm\]each done
clear
C)
\[50\,\,cm\]each and\[60\,\,cm\] done
clear
D)
Cannot be determined. done
clear
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question_answer16)
\[ABCD\]is a parallelogram as shown in the figure. If \[AB=2AD\] and \[P\] is the mid-point of\[AB\], find the measure of\[\angle CPD\].
A)
\[{{90}^{o}}\] done
clear
B)
\[{{60}^{o}}\] done
clear
C)
\[{{45}^{o}}\] done
clear
D)
\[{{135}^{o}}\] done
clear
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question_answer17)
In a parallelogram\[ABCD\], if \[AB=2x+5,\] \[CD=y+1,\] \[AD=y+5\] and\[BC=3x-4\], what is the ratio of \[AB\] and\[BC\]?
A)
\[71:21\] done
clear
B)
\[12:11\] done
clear
C)
\[31:35\] done
clear
D)
\[4:7\] done
clear
View Solution play_arrow
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question_answer18)
When is the quadrilateral formed by joining the midpoints of the sides of a quadrilateral\[PQRS\], taken in order, a rectangle?
A)
\[PQRS\] is a rectangle. done
clear
B)
\[PQRS\]is a parallelogram. done
clear
C)
Diagonals of \[PQRS\] are perpendicular. done
clear
D)
Diagonals of \[PQRS\] are equal. done
clear
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question_answer19)
The diagonals of a parallelogram \[ABCD\] intersect at\[O\]. If \[\angle BOC={{90}^{o}}\] and\[\angle BDC={{50}^{o}}\], find\[\angle OAB\].
A)
\[{{10}^{o}}\] done
clear
B)
\[{{40}^{o}}\] done
clear
C)
\[{{50}^{o}}\] done
clear
D)
\[{{90}^{o}}\] done
clear
View Solution play_arrow
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question_answer20)
If \[ABCD\] is an isosceles trapezium, what is\[\angle C\] equal to?
A)
\[\angle B\] done
clear
B)
\[\angle A\] done
clear
C)
\[\angle D\] done
clear
D)
\[{{90}^{o}}\] done
clear
View Solution play_arrow
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question_answer21)
When is the quadrilateral formed by joining the midpoints of the sides of a quadrilateral\[PQRS\], taken in order, a rhombus?
A)
\[PQRS\] is a rhombus. done
clear
B)
\[PQRS\]is a parallelogram. done
clear
C)
Diagonals of \[PQRS\] are perpendicular. done
clear
D)
Diagonals of \[PQRS\] are equal. done
clear
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question_answer22)
If angles \[P,\,\,Q,\,\,R\] and \[S\] of the quadrilateral\[PQRS\], taken in order, are in the ratio\[3:7:6:4\], what is\[PQRS\]?
A)
A rhombus done
clear
B)
A parallelogram done
clear
C)
A trapezium done
clear
D)
A kite done
clear
View Solution play_arrow
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question_answer23)
If \[PQ\] and \[RS\] are two perpendicular diameters of a circle, what is\[PRQS\]?
A)
A rectangle done
clear
B)
A trapezium done
clear
C)
A square done
clear
D)
A rhombus but not a square done
clear
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question_answer24)
What is the number of measurements required to construct a quadrilateral?
A)
\[5\] done
clear
B)
\[4\] done
clear
C)
\[3\] done
clear
D)
\[2\] done
clear
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question_answer25)
If the lengths of two diagonals of a rhombus are \[12\,\,cm\] and\[16\,\,cm\], find the length of each side of the rhombus.
A)
\[10\,\,cm\] done
clear
B)
\[14\,\,cm\] done
clear
C)
\[16\,\,cm\] done
clear
D)
\[8\,\,cm\] done
clear
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question_answer26)
In a rhombus\[ABCD\], \[\angle A={{60}^{o}}\] and\[AB=6\,\,cm\]. Find the diagonal\[BD\].
A)
\[2\sqrt{3}cm\] done
clear
B)
\[6\,\,cm\] done
clear
C)
\[12\,\,cm\] done
clear
D)
Insufficient data done
clear
View Solution play_arrow
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question_answer27)
In a parallelogram\[ABCD\], \[AB=4\,\,cm\] and\[BC=7\,\,cm\]. Each of its diagonals is less than which of the following?
A)
\[3\,\,cm\] done
clear
B)
\[4\,\,cm\] done
clear
C)
\[7\,\,cm\] done
clear
D)
\[11\,\,cm\] done
clear
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question_answer28)
Which of the following is not true for a parallelogram?
A)
Opposite sides are equal. done
clear
B)
Opposite angles are equal. done
clear
C)
Opposite angles are bisected by the diagonals. done
clear
D)
Diagonals bisect each other. done
clear
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question_answer29)
\[APB\] and \[CQD\] are parallel lines and a transversal \[PQ\] cuts them at \[P\] and\[Q\]. Which of the following is formed by the bisectors of angles \[APQ,\,\,BPQ,\,\,CQP\] and\[PQD\]?
A)
A rectangle done
clear
B)
A rhombus done
clear
C)
A square done
clear
D)
Any other parallelogram done
clear
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question_answer30)
\[PQRS\]is a quadrilateral. \[PR\] and \[QS\] intersect each other at\[O\], In which of the following cases is PQRS a parallelogram?
A)
\[\angle P={{100}^{o}},\,\,\angle Q={{80}^{o}},\,\,\angle R={{100}^{o}}\] done
clear
B)
\[\angle P={{85}^{o}},\,\,\angle Q={{85}^{o}},\,\,\angle R={{95}^{o}}\] done
clear
C)
\[PQ=7\,\,cm,\,\,QR=7\,\,cm,\,\,RS=8\,\,cm,\]\[OS=5.2\,\,cm\] done
clear
D)
\[OP=6.5\,\,cm,\,\,OQ=6.5\,\,cm,\,\,OR=5.2\,\,cm,\] \[OS=5.2\,\,cm\] done
clear
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question_answer31)
In a quadrilateral, the angles, \[A,\,\,B,\,\,C\] and \[D\] are in the ratio\[1:2:3:4\]. What is the measure of the largest angle of the quadrilateral?
A)
\[{{135}^{o}}\] done
clear
B)
\[{{144}^{o}}\] done
clear
C)
\[{{154}^{o}}\] done
clear
D)
\[{{108}^{o}}\] done
clear
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question_answer32)
\[ABCD\] is a rhombus such that one of its diagonals is equal to its side. Find the measure of the angles of rhombus\[ABCD\].
A)
\[{{45}^{o}},\,\,{{135}^{o}},\,\,{{45}^{o}},\,\,{{135}^{o}}\] done
clear
B)
\[{{100}^{o}},\,\,{{80}^{o}},\,\,{{100}^{o}},\,\,{{80}^{o}}\] done
clear
C)
\[{{120}^{o}},\,\,{{60}^{o}},\,\,{{120}^{o}},\,\,{{60}^{o}}\] done
clear
D)
\[{{60}^{o}},\,\,{{60}^{o}},\,\,{{60}^{o}},\,\,{{60}^{o}}\] done
clear
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question_answer33)
Which of the following is not a property of a rhombus?
A)
All four sides are equal. done
clear
B)
Diagonals bisect each other. done
clear
C)
Diagonals bisect opposite angles. done
clear
D)
One angle between the diagonals is\[{{60}^{o}}\] done
clear
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question_answer34)
I All the angles of a convex quadrilateral are congruent. However, not all sides are congruent. What type of a quadrilateral is it?
A)
Parallelogram done
clear
B)
Square done
clear
C)
Rectangle done
clear
D)
Trapezium done
clear
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question_answer35)
In quadrilateral\[ABCD,\]\[\angle A={{38}^{o}}\], \[\angle C=3\angle A\]and\[\angle D=4\angle A\]. Find the value of\[\angle B\].
A)
\[{{56}^{o}}\] done
clear
B)
\[{{304}^{o}}\] done
clear
C)
\[{{52}^{o}}\] done
clear
D)
\[{{114}^{o}}\] done
clear
View Solution play_arrow
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question_answer36)
In the given figure, \[p,\,\,q\] and \[r\] are three parallel lines. \[l\] and \[m\] are two transversals, such that \[DE=1.5\,\,cm\]\[,\] \[EF=3\,\,cm\]. Find \[BC\] if\[AB=2.5\,\,cm\].
A)
\[4\,\,cm\] done
clear
B)
\[5.5\,\,cm\] done
clear
C)
\[5\,\,cm\] done
clear
D)
\[6\,\,cm\] done
clear
View Solution play_arrow
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question_answer37)
\[ABCD\] is a rectangle with\[\angle ABD={{40}^{o}}\]. Find\[\angle DBC\].
A)
\[{{45}^{o}}\] done
clear
B)
\[{{30}^{o}}\] done
clear
C)
\[{{50}^{o}}\] done
clear
D)
\[{{35}^{o}}\] done
clear
View Solution play_arrow
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question_answer38)
Find the measure of each angle of a parallelogram, if one of its angles is \[{{30}^{o}}\] less than twice the smallest angle.
A)
\[{{70}^{o}},\,\,{{110}^{o}},\,\,{{70}^{o}},\,\,{{110}^{o}}\] done
clear
B)
\[{{70}^{o}},\,\,{{110}^{o}},\,\,{{80}^{o}},\,\,{{110}^{o}}\] done
clear
C)
\[{{120}^{o}},\,\,{{60}^{o}},\,\,{{120}^{o}},\,\,{{60}^{o}}\] done
clear
D)
\[{{100}^{o}},\,\,{{80}^{o}},\,\,{{100}^{o}},\,\,{{80}^{o}}\] done
clear
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question_answer39)
Which of the following pairs of angles are opposite angles of a cyclic quadrilateral?
A)
\[{{131}^{o}},\,\,{{28}^{o}}\] done
clear
B)
\[{{95}^{o}},\,\,{{55}^{o}}\] done
clear
C)
\[{{123}^{o}},\,\,{{57}^{o}}\] done
clear
D)
\[{{64}^{o}},\,\,{{52}^{o}}\] done
clear
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question_answer40)
Two adjacent angles of rhombus are \[3x-{{40}^{o}}\] and\[2x+{{20}^{o}}\]. Find the measurement of the greater angle.
A)
\[{{160}^{o}}\] done
clear
B)
\[{{100}^{o}}\] done
clear
C)
\[{{80}^{o}}\] done
clear
D)
\[{{120}^{o}}\] done
clear
View Solution play_arrow
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question_answer41)
If \[PQRS\] is a parallelogram, find the value of\[\angle Q-\angle S\].
A)
\[{{90}^{o}}\] done
clear
B)
\[{{120}^{o}}\] done
clear
C)
\[{{180}^{o}}\] done
clear
D)
\[{{0}^{o}}\] done
clear
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question_answer42)
If the degree measures of the angles of a quadrilateral are \[4x,\,\,7x,\,\,9x\] and\[10x\], what is the sum of the measures of the smallest angle and the largest angle?
A)
\[{{140}^{o}}\] done
clear
B)
\[{{150}^{o}}\] done
clear
C)
\[{{168}^{o}}\] done
clear
D)
\[{{180}^{o}}\] done
clear
View Solution play_arrow
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question_answer43)
In a quadrilateral ABCD, diagonals bisect each other at right angles. If\[AB=BC=AD=6\,\,cm\], find the length of\[CD\].
A)
\[3\,\,cm\] done
clear
B)
\[6\,\,cm\] done
clear
C)
\[6\sqrt{2}cm\] done
clear
D)
\[12\,\,cm\] done
clear
View Solution play_arrow
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question_answer44)
In \[\Delta ABC\]\[,\] \[\angle A={{50}^{o}}\]\[,\]\[\angle B={{60}^{o}}\]and\[\angle c={{70}^{o}}\]. Find the measures of the angles of the triangle formed by joining the mid-points of the sides of\[\Delta ABC\].
A)
\[{{90}^{o}}\] done
clear
B)
\[{{120}^{o}}\] done
clear
C)
\[{{180}^{o}}\] done
clear
D)
\[{{0}^{o}}\] done
clear
View Solution play_arrow
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question_answer45)
In a quadrilateral three angles are in the ratio \[3:3:1\] and the fourth angle is\[{{80}^{o}}\]. Find the measure of the other angles.
A)
\[{{120}^{o}},\,\,{{120}^{o}},\,\,{{40}^{o}}\] done
clear
B)
\[{{100}^{o}},\,\,{{100}^{o}},\,\,{{80}^{o}}\] done
clear
C)
\[{{110}^{o}},\,\,{{110}^{o}},\,\,{{60}^{o}}\] done
clear
D)
\[{{90}^{o}},\,\,{{90}^{o}},\,\,{{30}^{o}}\] done
clear
View Solution play_arrow
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question_answer46)
\[JUMP\] is a square with\[\angle JUP={{45}^{o}}\]. Find\[\angle PUM\].
A)
\[{{45}^{o}}\] done
clear
B)
\[{{90}^{o}}\] done
clear
C)
\[{{35}^{o}}\] done
clear
D)
\[{{15}^{o}}\] done
clear
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question_answer47)
In\[\Delta DEF\], \[PQ\] is a line segment drawn through mid-points of \[DE\] and\[DF\]respectively. If\[EF=7.6\,\,cm\], find the length of\[PQ\].
A)
\[3.8\,\,cm\] done
clear
B)
\[4.5\,\,cm\] done
clear
C)
\[7.2\,\,cm\] done
clear
D)
\[2.6\,\,cm\] done
clear
View Solution play_arrow
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question_answer48)
In quadrilateral \[ABCD\], \[\angle B={{90}^{o}},\,\,\angle C-\angle D\]\[={{60}^{o}}\]and\[\angle A-\angle C-\angle D={{10}^{o}}\]. Find\[\angle A\], \[\angle C\]and\[\angle D\].
A)
\[{{140}^{o}},\,\,{{95}^{o}},\,\,{{35}^{o}}\] done
clear
B)
\[{{95}^{o}},\,\,{{70}^{o}},\,\,{{65}^{o}}\] done
clear
C)
\[{{25}^{o}},\,\,{{45}^{o}},\,\,{{105}^{o}}\] done
clear
D)
\[{{150}^{o}},\,\,{{20}^{o}},\,\,{{35}^{o}}\] done
clear
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question_answer49)
Two angles of a quadrilateral are \[{{60}^{o}}\] \[\text{are}\] \[{{70}^{o}}\] and other two angles are in the ratio of\[8:15\]. Which of the following are the remaining two angles?
A)
\[{{80}^{o}},\,\,{{150}^{o}}\] done
clear
B)
\[{{90}^{o}},\,\,{{140}^{o}}\] done
clear
C)
\[{{100}^{o}},\,\,{{130}^{o}}\] done
clear
D)
\[{{110}^{o}},\,\,{{120}^{o}}\] done
clear
View Solution play_arrow
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question_answer50)
In quadrilateral\[ABCD\]\[,\] \[\angle A+\angle C={{140}^{o}}\], \[\angle A:\]\[\angle C=1:3\]and\[\angle B:\angle D=5:6\]. Find the measures of\[\angle A,\,\,\angle B,\,\,\angle C\]and\[\angle D\].
A)
\[{{35}^{o}},\,\,{{100}^{o}},\,\,{{105}^{o}},\,\,{{120}^{o}}\] done
clear
B)
\[{{60}^{o}},\,\,{{45}^{o}},\,\,{{75}^{o}},\,\,{{100}^{o}}\] done
clear
C)
\[{{20}^{o}},\,\,{{60}^{o}},\,\,{{105}^{o}},\,\,{{135}^{o}}\] done
clear
D)
\[{{45}^{o}},\,\,{{35}^{o}},\,\,{{90}^{o}},\,\,{{110}^{o}}\] done
clear
View Solution play_arrow
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question_answer51)
If an angle of a parallelogram is four-fifths of its adjacent angle, find the angles of the parallelogram.
A)
\[{{60}^{o}},\,\,{{120}^{o}},\,\,{{60}^{o}},\,\,{{120}^{o}}\] done
clear
B)
\[{{90}^{o}},\,\,{{90}^{o}},\,\,{{90}^{o}}\] done
clear
C)
\[{{80}^{o}},\,\,{{100}^{o}},\,\,{{80}^{o}},\,\,{{100}^{o}}\] done
clear
D)
\[{{30}^{o}},\,\,{{150}^{o}},\,\,{{30}^{o}},\,\,{{100}^{o}}\] done
clear
View Solution play_arrow
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question_answer52)
\[ABCD\] is a rhombus in which \[AC=16\,\,cm\] and \[BC=10\,\,cm\]. Find the length of the diagonal\[BD\]
A)
\[16\,\,cm\] done
clear
B)
\[8\,\,cm\] done
clear
C)
\[12\,\,cm\] done
clear
D)
\[10\,\,cm\] done
clear
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question_answer53)
\[ABCD\] is a parallelogram. The angle bisectors of \[\angle A\] and \[\angle D\] intersect at\[O\]. Find the measure of\[\angle AOD\].
A)
\[{{75}^{o}}\] done
clear
B)
\[{{45}^{o}}\] done
clear
C)
\[{{90}^{o}}\] done
clear
D)
\[{{180}^{o}}\] done
clear
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question_answer54)
In quadrilateral\[PQRS\]\[,\]\[\angle P+\angle R={{140}^{o}}\] and\[\angle Q:\angle S=5:6\]. Find\[\angle Q\].
A)
\[{{100}^{o}}\] done
clear
B)
\[{{120}^{o}}\] done
clear
C)
\[{{105}^{o}}\] done
clear
D)
\[{{35}^{o}}\] done
clear
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question_answer55)
\[E\] and \[F\] are the midpoints of the sides \[AB\] and \[AC\] respectively of ; G and H are midpoints of the sides AE and AF respectively of \[\Delta AEF.\]If GH = 1.8 cm, find BC.
A)
0.9 cm done
clear
B)
3.6 cm done
clear
C)
7.2 cm done
clear
D)
5.4 cm done
clear
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question_answer56)
Two opposite angles of a parallelogram are \[{{(3p-4)}^{o}}\]and\[{{(48-p)}^{o}}.\]What is the value of p?
A)
13 done
clear
B)
15 done
clear
C)
17 done
clear
D)
20 done
clear
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question_answer57)
In the given figure, \[\Delta ABC\]and \[\Delta DEF\]are such that\[AB=DE,\,BC=EF,\]and BC//EF. What is ADFC?
A)
A square done
clear
B)
A rectangle done
clear
C)
A parallelogram done
clear
D)
A rhombus done
clear
View Solution play_arrow