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 line joining the mid points of the diagonals of a trapezium has length $3$cm. If the longer base is $97$cm then the shorter base is:

  1. $94$cm
  2. $92$cm
  3. $91$cm
  4. $90$cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The line joining the mid point of the diagonals of a trapezium is half the length of the difference between the two sides.
Let the smaller side be $x$
Then, $3 = \dfrac{97 -x}{2}$
$6= 97 - x$
$x = 91$ cm

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

The consecutive angles of a trapezium form an arithmetic sequence. If the smallest angle is $\displaystyle 75^{\circ}$, then the largest angle is

  1. $\displaystyle 100^{\circ}$
  2. $\displaystyle 105^{\circ}$
  3. $\displaystyle 110^{\circ}$
  4. $\displaystyle 115^{\circ}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Since, sum of all the four angles of a quadrilateral is $360^o$.

Angle 1 $=75^o$, Angle 2 $=75^o+x$, Angle 3 $=75^o+2x$, Angle 4 $=75^o+3x$
Angle 1 $+$ Angle 2 $+$ Angle 3 $+$ Angle 4 $=360^o$
$\therefore   75^o+75^o+x+75^o+2x+75^o+3x=360^o$
$\Rightarrow 300+6x=360\Rightarrow 6x=60 \Rightarrow x=10$
$\therefore$ Largest angle (Angle 4)$=75^o+3x=75^o+3\times 10=105^o$

Hence, option B.

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

In isoceles trapezoid ABCD, side CD is parallel to to side AB, line segment AC is congruent to line segment BD.The degree measure of angle BDC = $80^o$. Find the measures of the $\angle A$.

  1. $90^o$
  2. $100^o$
  3. $110^o$
  4. $120^o$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

As per the property of isosceles trapezoid, 
Opposite sides of an isosceles trapezoid are the same length (congruent) and the angles on either side of the bases are the same size (congruent).
So, Angle C = $80^o$
Since the top and bottom angles are supplementary, we know that,
Angle A = $180 - 80$
Angle A = $100^o$
Similarly, the Angle of B = $100^o$

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

State whether true or false:

All trapeziums are parallelograms.

  1. True

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

There is some disagreement whether parallelograms, which have two pairs of parallel sides, should be regarded as trapezoids. Some define a trapezoid as a quadrilateral having only one pair of parallel sides (the exclusive definition), thereby excluding parallelograms

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

In the trapezium PQRS, PQ is  parallel to RS and the diagonals intersect at O. If $OP.SR= m(OR . PQ)$, then the value of m is :

  1. $\dfrac{1}{4}$
  2. $\dfrac{1}{3}$
  3. $1$
  4. $\dfrac{1}{2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In Trapezium PQRS, $\Delta OPQ$ is similar to $\Delta OSR$ by AA similarity.
$\therefore \dfrac{OP}{OR}=\dfrac{OS}{OQ}=\dfrac{PQ}{SR}$
$\therefore OP.SR=OR.PQ$
Hence, $m=1$

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

The parallel sides of a trapezium are $x$ and $y$ in length. The length of the line segment joining the mid points of the non parallel sides is:

  1. $\dfrac{x+y}{2}$
  2. $x+y$
  3. $\dfrac{2x+3y}{2}$
  4. $\dfrac{xy}{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The line segment joining the mid points of non parallel sides of a trapezium is the average of sum of the parallel sides.
Hence, $= \dfrac{x+y}{2}$