Tag: closed figures

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Questions Related to closed figures

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

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

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

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

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 

  1. parallelogram

  2. rhombus

  3. trapezium

  4. kite
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

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

  1. parallelogram

  2. rhombus

  3. square

  4. trapezium
Reveal answer Fill a bubble to check yourself
D Correct answer
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.

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

If $ABCD$ is an isosceles trapezium $\displaystyle \angle C$ is equal to:

  1. $\displaystyle \angle B$
  2. $\displaystyle \angle A$
  3. $\displaystyle \angle D$

  4. Depends on the naming of the trapezium
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$Properties\  of \ an \ isosceles\  trapezium:  $

It has a pair of parallel sides.

It has a pair of opposite sides that are congruent.

Both pairs of opposite angles are supplementary, that is they sum to $180°$.

Consecutive angles along both bases are congruent.

Diagonals are congruent.

$\therefore $In an isosceles trapezium the base angles are always equal. Hence, it depends how we name an isosceles trapezium.

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

A quadrilateral-shaped photo-frame has all sides equal. Which of the following is not a possible shape for the photo-frame.

  1. Square

  2. Trapezium

  3. Rhombus

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
A trapezium is a quadrilateral having one pair of opposite sides parallel. The other pair of opposite sides are non parallel and equal. Hence , the photo frame can be a square or a rhombus where all the sides are equal. The shape of the photo frame can not be a trapezium.
Multiple choice maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

In trapezium $ABCD$ has $AD$ parallel to $BC,AC$ and $BD$ intersect at $P$. If $\dfrac {[ADP]}{[BCP]}=\dfrac {1}{2}$, find $\dfrac {[ADP]}{[ABCD]}$. (Here the notion $[P _{1}...P _{n}]$ denotes the area of the polygon ) $[P _{1}...P _{n}]$

  1. $2-\sqrt {3}$
  2. $3-2\sqrt {2}$
  3. $\sqrt {3}-\sqrt {2}$
  4. $2(\sqrt {3}-\sqrt {2})$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The ratio of areas of triangles formed by diagonals in a trapezium is the square of the ratio of the parallel sides. The calculation leads to the provided value.