Free Understanding Quadrilaterals 03 Practice Test - 8th Grade 

The pentagon has the most number of vertices among the options. Hence, it has the most number of diagonals.

A concave polygon will have some part of at least one diagonal external. 

A regular polygon is a polygon which is equiangular i.e. all the angles are equal and equilateral i.e. all the sides are equal.

The triangle if equilateral is a regular polygon. If not, it is not a regular polygon.

A rhombus has equal sides but not equal angles.

A Rectangle has equal angles but not equal sides. Hence, they are not regular polygons.

A square has equal sides and equal angles. Hence, it is a regular polygon.

The statement that all squares are rectangles is true because a square is a special type of rectangle where, the adjacent sides are equal. 

Let$\angle A=x^{\circ }$
then $\angle D=(180-x{)}^{\circ }$
(Since the adjacent angles of a parallelogram sum up to ${180}^{\circ })$

$\therefore \frac{\angle A}{2}=\frac{x}{2}=\angle DAO$
and$\frac{\angle D}{2}=\frac{(180-x)}{2}=90-\frac{x}{2}=\angle ADO$

In $\Delta AOD,$

$\angle AOD+\angle ADO+\angle DAO={180}^{\circ }$   [Angle sum property of a triangle]
$\angle AOD={180}^{\circ }-[\angle ADO+\angle DAO]$  
$\angle AOD={180}^{\circ }-[\frac{x}{2}+90-\frac{x}{2}]$
$or\angle AOD=180-90={90}^{\circ }$
$\therefore$ The measure of $\angle AOD$ is ${90}^{\circ }$

The body of a car is a 3 dimensional surface. It is not a plane 2 dimensional surface

Let ‘a’ be one side of the kite = 7.8 cm
and‘b’ be the other side of the kite = 11 cm
Perimeter of the kite = 2a + 2b units
$=2\times 7.8+2\times 11=15.6+22=37.6cm$

The kites that have all the sides equal and two pairs of sides parallel are parallelograms. These kites are rhombuses.

Hence, some kites are parallelograms.