Question 2 :
Can the angles $110^o, 80^o, 90^o$ & $105^o$ be the angles of quadrilateral?
Question 3 :
The adjacent sides of a parallelogram are 15 cm and 10 cm. If length of one diagonal of this parallelogram is 20 cm, the length of other diagonal will be
Question 8 :
Given that ABCD is a parallelogram. If AC is perpendicular to BD but is not equal to it then ABCD is a Rhombus.<br/>
Question 9 : Match the following.<table class="wysiwyg-table"><tbody><tr><td>$(1)$ Rectangle</td><td>(p) A quadrilateral having its opposite sides equal and parallel.</td></tr><tr><td>$(2)$ Square</td><td>(q) A parallelogram having its opposite sides equal and each of the angle is a right angle.</td></tr><tr><td>$(3)$ Parallelogram</td><td>(r) A parallelogram having all sides equal and each of the angle is a right angle.</td></tr><tr><td>$(4)$ Rhombus</td><td>(s) A quadrilateral in which a pair of opposite sides are parallel.</td></tr><tr><td>$(5)$ Trapezium</td><td>(t) A parallelogram having all sides equal.</td></tr></tbody></table>
Question 10 :
The diagonals of a quadrilateral are equal and bisect each other. The quadrilateral has to be
Question 11 :
Two parallelograms stand on equal bases and between the same parallels. The ratio of their areas is
Question 12 :
Three vertices of a parallelogram are $(a+b,a-b), (2a+b, 2a-b), (a-b, a+b)$. Find the fourth vertex.
Question 13 :
The measure of an angle of a parallelogram is $70^0$. Find its remaining angles.
Question 14 :
Name the quadrilaterals whose diagonals bisect each other<br/><br/><b>Answer: </b>Parallelogram; rhombus; square; rectangle.<br/>
Question 15 :
If the perimeter of a parallelogram is $50$ cm and one side is $12$ cm. what is the measure of the other side ?
Question 16 :
A quadrilateral whose each angle is a right angle is a
Question 17 :
There exists a quadrilateral with a rotational symmetry of the order more than 1 but doesn't have a line symmetry.
Question 18 :
In a square ABeD, its diagonals bisect at O. Then the triangleAOB is
Question 19 :
What is the maximum possible area of a parallelogram with one side of length 2 meters and a perimeter of 24 meters ?
Question 20 :
The dimensions of rectangular field are $23x-10$ and $14x+8$ units. The values of $x$ for which it would be square is
Question 21 :
Three angles of a quadrilateral are $75^{\circ}, 90^{\circ}$ and $75^{\circ}$. The measure of fourth angle is?<br/>
Question 22 :
PQRS is a parallelogram and $\angle 1$ and $\angle 2$ are two exterior,angles, then $\angle 1=\angle 2=\angle 3=\angle 4$
Question 26 :
State true or false:A diagonal divides a parallelogram into two triangles of equal areas.
Question 27 :
If an angle of a parallelogram is 24$^o$ less than twice the smallest angle, then the value of largest angle of the parallelogram is
Question 30 :
Find the midpoint of the segment connecting the points $(a, -b)$ and $(5a, 7b)$.
Question 31 :
The perimeter of a parallelogram is ...................... when the sides are $12$ cm and $5$ cm.
Question 34 :
A quadrilateral has distinct integer side lengths. If the second-largest side has length $10$,then the maximum possible length of the largest side is<br>
Question 35 :
Three vertices of a parallelogram taken in order are $( - 1 , - 6 ) , ( 2 , - 5 )$ and $(7,2).$ The fourth vertex is :
Question 36 :
What is the sum of the measures of the angles of a convex quadrilateral? Will this property hold if the quadrilateral is not convex?<br>
Question 37 :
The four angles of a quadrilateral are as $3 : 5 : 7 :9$. Find the angles<br/>
Question 38 :
Fill in the blank:<br/>Line joining the mid-points of any two sides of a triangle is _____ to the third side.<br/>
Question 41 :
Which of the following is correct regarding the diagonals of a rhombus ?
Question 42 :
Two consecutive angles of parallelogram are in the ratio 1 : 3 Then the smaller angle is
Question 43 :
One side of a parallelogram is 8 cm. If thecorresponding altitude is 6 cm, then its area is given by
Question 44 :
ABCD is a rectangle such that $AC+AB=5 AD$ and $AC-AD=8$, then the area of rectangle ABCD is 
Question 45 :
The diagonals of rhombus are $24$ cm and $10$ cm. Then its perimeter is:
Question 46 :
State true or false:<br/>In a parallelogram, the diagonals intersect at right angles
Question 47 :
If two parallel lines are cut by two distinct transversals, then the quadrilateral formed by these four lines will always be a:
Question 48 :
Fill in the blanks:<br/>(i) The ling segment joining a vertex of a triangle to the midpoint of its opposite side is called a $\underline { P } $ of the triangle.<br/>(ii) The perpendicular line segment from a vertex of a triangle to its opposite is called an $\underline { Q } $ of the triangle<br/>(iii) A triangle has $\underline { R } $ altitudes and $\underline { S } $ medians
Question 49 :
State whether the given Question is True or False?The diagonals of a parallelogram bisect each other.
Question 50 :
What is the maximum possible area of a parallelogram with one side of length 2 meters and a perimeter of 24 meters ?
Question 51 :
The measures of angles of a quadrilateral in degrees are $x, 3x - 40 , 2x$ and $4x +20$. Find the measure of each angle.
Question 52 :
If two sides of a parallelogram are $6$ and $8$ and one diagonal is $7$, what is the length of the other diagonal?
Question 53 :
If $(3, -4)$ and $(-6, 5)$ are the extremities of a diagonal of a parallelogram and $(2, 1)$ is its third vertex , then its forth vertex is
Question 54 :
Let ABCD be a parallelogram such that AB = q , AB = p, and $\angle BAD $ be an acute angle. If r is the vector that coincides with the altitude directed from the vertex B to the side AD, then r is given by
Question 55 :
Let ABCD be a parallelogram such that AB = q , AB = p, and $\angle BAD $ be an acute angle. If r is the vector that coincides with the altitude directed from the vertex B to the side AD, then r is given by
Question 56 :
$T_{m} $denotes the number of Triangles that can be formed with the vertices of a regular polygon of $m$ sides. If $T_{m+1}-T_{m}=15, $then $m=$<br><br>
Question 57 :
A has a pair of triangles with corresponding sides proportional, and B has a pair of pentagons with corresponding sides proportional.<br>$S_1\equiv$A's triangles must be similar<br>$S_2\equiv$ B's pentagons must be similar<br>Which of the following statement is correct?
Question 58 :
$ABCD$ is a parallelogram $P$ is a point on $AB$ such that $AP : PB = 3 : 2$. $Q$ is a point on $CD$ such that $CQ : QD = 7 : 3$. If $PQ$ meets $AC$ at $R$, then $AR : AC$ is
Question 59 :
The two diagonals of a rhombus are $24$ cm and $10$ cm long. The length of each side of the rhombus is
Question 60 :
The number of sides in a polygon of equal distance whose one interior angle is 108 will be
Question 61 :
The point of intersection of the diagonals of a quadrilateral divides one diagonal in theratio $1 : 2 .$ Can it be a parallelogram?
Question 62 :
ABCD is a square with side a. With centres A, B, C and D four circles are drawn such that each circle touches externally two of the remaining three circles. Let $\delta$ be the area of the region in the interior of the square and exterior of the circles. Then the maximum value of $\delta$ is
Question 64 :
A cross section at the midpoint of the middle piece of a human sperm will show
Question 65 :
If $\vec{a}$ and $\vec{b}$ are adjacent side of parallelogram , then $|\vec{a} + \vec{b}| = |\vec{a} - \vec{b}|$ is necessary and sufficient condition for a parallelogram to be a
Question 66 :
A school was having 4 Hexagonal buildings joined to each other. They wanted to utilize the space between the 4 buildings to make a playground. The shape is that of a parallelogram. Can you find the measure of the angles as opposite angles are equal?
