If angles $A, B, C$ and $D$ of the quadrilateral $ABCD$,taken in order,are in the ratio $3:7:6:4$,then $ABCD$ is a

$(1)$ If no three points out of four coplanar points are collinear,then a $\ldots \ldots \ldots$ figure formed by joining these four points in order is called a quadrilateral.
$(2)$ $A$ quadrilateral has $\ldots \ldots \ldots$ pairs of opposite sides.

Prove that in a parallelogram,the bisectors of any two consecutive angles intersect at right angles.

$A$ square is inscribed in an isosceles right triangle so that the square and the triangle have one angle common. Show that the vertex of the square opposite the vertex of the common angle bisects the hypotenuse.

$D, E$ and $F$ are the mid-points of the sides $BC, CA$ and $AB$ respectively of an equilateral triangle $ABC$. Show that $\triangle DEF$ is also an equilateral triangle.

$P$ is the mid-point of the side $CD$ of a parallelogram $ABCD$. $A$ line through $C$ parallel to $PA$ intersects $AB$ at $Q$ and $DA$ produced at $R$. Prove that $DA = AR$ and $CQ = QR$.