Tag: when lines join

Quizzes (3) Questions (42)

Questions Related to when lines join

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

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 :

  1. 12

  2. 13

  3. 14

  4. 17
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

By the triangle inequality and the properties of a trapezium, the possible integral values for the fourth side x are constrained by the lengths of the parallel sides.

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.