Mahabir Singh Solutions for Chapter: Quadrilaterals, Exercise 1: MATHEMATICAL REASONING

The measure of all the angles of a parallelogram, if an angle adjacent to the smallest angle is $24°$ less than twice the smallest angle is

The quadrilateral formed by joining the mid-points of the sides of a quadrilateral $PQRS$, taken in order is rectangle if,

$ABCD$ is a parallelogram. If $AB$ is produced to $E$ such that $ED$ bisects $BC$ at $O$, then which of the following is correct?

$D$ And $E$ are the mid-points of the sides $AB$ and $AC$, respectively of $△ABC$. $DE$ is produced to $F.$ To Prove that $CF$ is equal and parallel to $DA,$we need an additional information which is-

$X,Y$ Are the mid-points of opposite sides $AB$ and $DC$ of a parallelogram $ABCD$. $AY$ And $DX$ are joined intersecting in $S;$ $CX$ and $BY$ joined intersecting in $R$. Then $SXRY$ is a

In a given figures, if $ABCD$ is a rectangle and $P,Q$ are the mid-points of $AD,DC$ respectively. Then, the ratio of lengths $PQ$ and $AC$ is equal to

In the given figure, $ABCD$ is a parallelogram in which $P$is the mid-point of $DC$ and $Q$is a point on $AC$ such that $CQ=\frac{1}{4}AC$and $PQ$product meet $BC$ at $R$, then,

If $APB$ and $CQD$ are two parallel lines, then the bisectors of the angles $APQ,BPQ,CQP$ and $PQD$ form a