Tag: when lines join

Questions Related to when lines join

With compasses and ruler, construct with each of the following angles:

maths when lines join set squares constructing a perpendicular bisector construction of a perpendicular bisector

  1. 60 $ ^{\circ} $

  2. 30 $ ^{\circ} $

  3. 90 $ ^{\circ} $

  4. 45 $ ^{\circ} $

  5. 22 $\frac{1}{2} ^{\circ} $

  6. 75 $ ^{\circ} $

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Correct Option: A
State True or False:
An angle of $52.5$ can be constructed using the compass.
maths when lines join set squares constructing a perpendicular bisector construction of a perpendicular bisector

  1. True

  2. False

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Correct Option: A
Explanation:

 As $52.5 =\frac{210^{\circ}}{4} \ and \   210 =180 + 30 $  and we can bisect the angle, so given angle can be constructed.

So True.

$ABCD$ is trapezium with $AB||DC=30cm$ and $AB=50cm$. If $X$ and $Y$ are the mid point of $AD$ and $BC$, then $ar(DCYX)=\dfrac {5}{9}ar(XYBA)$.

maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

  1. True

  2. False

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Correct Option: B

The length of the parallel sides of a trapezium are 14 cm and 7 cm. If the length of third side is 8 cm and of fourth sides is c xm, then the number of possible integral value of x is :

maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

  1. 12

  2. 13

  3. 14

  4. 17

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Correct Option: A

A quadrilateral having one and only one pair of parallel sides is called 

maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

  1. a parallelogram

  2. a kite

  3. a rhombus

  4. trapezoids

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Correct Option: D
Explanation:

Quadrilateral with one pair of parallel sides is a trapezoid. If it has two pairs of parallel sides it is a parallelogram, but parallelograms are also trapezoids.

State 'true' or 'false'

The diagonals of a trapezium bisect each other.

maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

  1. True

  2. False

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Correct Option: B
Explanation:

False.
Diagonals of trapezium does not bisect each other.

The angles of a quadrilateral are in the ratio $3:\ 4:\ 5:\ 6$. Then the quadrilateral is a trapezium.

maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

  1. True

  2. False

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Correct Option: A
Explanation:

$Let\angle A,\angle B,\angle C\quad and\angle D\quad be\quad the\quad angles\quad of\quad quadilateral\ \angle A=3x,\angle B=4x,\angle C=5x\quad and\angle D=6x,where\quad x\quad is\quad a\quad constantIn\quad quadilateral\quad ABCD\quad \ \angle A+\angle B+\angle C+\angle D=360(Angle\quad sum\quad property)\ 3x+4x+5x+6x=360\ 18x=360\ x=20\ \angle A=3x=3\times 20=60\ \angle B=4x=4\times 20=80\ \angle C=5x=5\times 20=100\ \angle D=6x=6\times 20=120$
$In\quad quadilateral\quad ABCD\quad \ \angle A+\angle D=60+120=180\ \angle B+\angle C=80+100=180\ \therefore AB\parallel CD(Sum\quad of\quad consecutive\quad interior\quad angle\quad is\quad supplementary)\ But\quad \angle A+\angle B=60+80\neq 180\ \therefore AB\quad is\quad not\quad parallel\quad to\quad BC\ Hence\quad quadilateral\quad is\quad a\quad trapzium(as\quad it\quad has\quad only\quad one\quad pair\quad of\quad parallel\quad side)$\

If the angles A, B, C and D of a quadrilateral ABCD in the same order are in the ratio 3 : 7 : 6 : 4, then ABCD is a 

maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

  1. parallelogram

  2. rhombus

  3. trapezium

  4. kite

Show answer
Correct Option: C
Explanation:

Let angles be $3x, 7x, 6x$ and $4x$
Total sum of angles of a quadrilateral = $360^{\circ}$
$\Rightarrow 3x + 7x + 6x + 4x = 360^{\circ}$
$\Rightarrow 20x = 360^{\circ}$
$\Rightarrow x = 18^{\circ}$
$\therefore$ Angles are $ 3\, \times\, 18^{\circ} = 54^{\circ}$
 $ 7\, \times\, 18^{\circ} = 126^{\circ}$
 $ 6\, \times\, 18^{\circ} = 108^{\circ}$
 $ 4\, \times\, 18^{\circ} = 72^{\circ}$
All the angles of the figure ABCD are different, thus it is a trapezium.
Hence, option 'C' is correct.

If two parallel lines are cut by two distinct transversals, then the quadrilateral formed by these four lines will always be a:

maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

  1. parallelogram

  2. rhombus

  3. square

  4. trapezium

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Correct Option: D
Explanation:

Let $p$ and $q$ be the two parallel lines cut by two distinct transversals $l$ and $m$. The figure formed by the lines $AB, BC, CD, DA$ will always be a trapezium as at least one pair of given lines will be parallel.

The diagonals of an isosceles trapezium are

maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

  1. unequal

  2. equal

  3. (1) and (2) both

  4. none of these

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Correct Option: B
Explanation:

An isosceles trapezium have equal opposite sides. Therefore diagonals of  trapezium are equal.