Tag: when lines join

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Questions Related to when lines join

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