Tag: when lines join

Questions Related to when lines join

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 :

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

  1. $\dfrac{1}{4}$

  2. $\dfrac{1}{3}$

  3. $1$

  4. $\dfrac{1}{2}$

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Correct Option: C
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, $m=1$

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:

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

  1. $\dfrac{x+y}{2}$

  2. $x+y$

  3. $\dfrac{2x+3y}{2}$

  4. $\dfrac{xy}{2}$

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Correct Option: A
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, $= \dfrac{x+y}{2}$