Tamil Nadu Board Solutions for Chapter: Geometry, Exercise 4: Exercise

$ABCD$ is a rectangle whose diagonals $AC$ and $BD$ intersect at $O$. If $\angle OAB=46°$, If $\angle OBC=k°$, then find the value of $k$.

The lengths of the diagonals of a rhombus are $12 \mathrm{cm}$ and $16 \mathrm{cm}$. Find the side of the rhombus.

Iron rods $a, b, c, d, e$, and $f$ are making a design in a bridge as shown in the figure. If $a\parallel b, c\parallel d, e\parallel f$, find the marked angles between $c$ and $f$.

In the given figure, $\angle A= 64° , \angle ABC=58°$. If $BO$ and $CO$ are the bisectors of $\angle ABC$ and $\angle ACB$ respectively of $△ABC$, find $x°$and $y°$.

In the given figure, if $AB=2, BC=6, AE=6, BF=8, CE=7$ and $CF=7$, then compute the ratio of the area of quadrilateral $ABDE$ to the area of $△CDF$.

In the given figure, $ABCD$ is a rectangle and $EFGH$ is a parallelogram. Using the measurements given in the figure, what is the length of the segment that is perpendicular to $\overline{HE}$  and $\overline{FG}$?

In the parallelogram $ABCD$ of the accompanying diagram, line $DP$ is drawn bisecting $BC$ at $N$ and meeting $AB$ (extended) at $P$. From vertex $C$, line $CQ$ is drawn bisecting side $AD$ at $M$ and meeting $AB$ (extended) at $Q$. Lines $DP$ and $CQ$ meet at $O$. Show that the area of triangle $QPO$ is $\frac{9}{8}$ of the area of the parallelogram $ABCD$.

In the following figure $ABCD$ is a parallelogram, $P$ and $Q$ are the midpoints of sides $AB$ and $DC$ respectively. Show that $APCQ$ is a parallelogram.