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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, $= \dfrac{x+y}{2}$

Multiple choice maths geometric sequences introduction to geometric progression understanding geometric progressions introduction to geometric progressions

A progression of the form $a, ar, ar^2$, ..... is a

  1. geometric series

  2. harmonic series

  3. arithmetic progression

  4. geometric progression
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A progression of the form $a, ar, ar^2$, ..... is a geometric progression.
Geometric Progression refers to a sequence in which successor term of each term is obtained by multiplying a constant term.

Multiple choice maths geometric sequences introduction to geometric progression understanding geometric progressions introduction to geometric progressions

The geometric progression which have infinite terms is called

  1. finite geometric progression

  2. finite arithmetic progression

  3. infinite geometric progression

  4. finite harmonic progression
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The geometric progression which have infinite terms is called infinite geometric progression.
$1 + 0.5 + 0.25 + 0.125....$ is an example of infinite geometric progression.