(B) Let $P, Q, R, S$ be the midpoints of sides $AB, BC, CD, DA$ respectively. By the Midpoint Theorem in $\triangle ABC$,$PQ \parallel AC$ and $PQ = \

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(B) Let $P, Q, R, S$ be the midpoints of sides $AB, BC, CD, DA$ respectively. By the Midpoint Theorem in $\triangle ABC$,$PQ \parallel AC$ and $PQ = \frac{1}{2} AC$. Similarly,in $\triangle ADC$,$SR \parallel AC$ and $SR = \frac{1}{2} AC$. Thus,$PQ \parallel SR$ and $PQ = SR$. Since one pair of opposite sides is equal and parallel,the quadrilateral $PQRS$ is a parallelogram. This result is known as the Varignon's Theorem.

Class 11 Mathematics Straight Lines Problems related to triangle and quadrilateral

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If $ABCD$ is a quadrilateral,and the midpoints of consecutive sides $AB, BC, CD$,and $DA$ are joined by straight lines to form a quadrilateral $PQRS$,then $PQRS$ is always:

A
Square
B
Parallelogram
C
Rectangle
D
Rhombus

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Problems related to triangle and quadrilateral

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DifficultJEE MAIN 2014

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Medium

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KVPY 2018

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KVPY 2015

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EasyAP EAMCET 2019

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If $ABCD$ is a quadrilateral,and the midpoints of consecutive sides $AB, BC, CD$,and $DA$ are joined by straight lines to form a quadrilateral $PQRS$,then $PQRS$ is always:

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Given three points $P, Q, R$ with $P(5, 3)$ and $R$ lies on the $x-$ axis. If the equation of $RQ$ is $x - 2y = 2$ and $PQ$ is parallel to the $x-$ axis,then the centroid of $\Delta PQR$ lies on the line

Without using the Pythagoras theorem,show that the points $(4,4), (3,5),$ and $(-1,-1)$ are vertices of a right-angled triangle.

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