Opposite Sides of a Parallelogram Are Equal

Q.

All squares are not parallelograms.

1. True
2. False

Q. A parallelogram having all sides equal is called a ______.

1. Trapezium
2. rhombus
3. rectangle
4. kite

Q. Question 8
ABCD is a quadrilateral in which AB || DC and AD = BC. Prove that $\angle A=\angle Band\angle C=\angle D$.

Q. Two adjacent sides of a parallelogram are 8 cm and 4 cm. What is its perimeter?

1. 20 cm
2. 28 cm
3. 24 cm
4. 30 cm

Q. Question 39
The sum of angles of a concave quadrilateral is
a) More than ${360}^{\circ }$
b) Less than ${360}^{\circ }$
c) Equal to ${360}^{\circ }$
d) Twice of ${360}^{\circ }$

Q.

The perimeter of a parallelogram is 22 cm. If the longer side measures 6.5 cm, what is the measure of the shorter side.

Q. Which of the following quadrilaterals two pairs of opposite sides parallel?

1. Square
2. Rhombus
3. Parallelogram
4. Rectangle

Q.

All parallelograms are trapeziums

1. True
2. False

Q. Ratio of two adjacent sides of a parallelogram is 3 : 4, and its perimeter is 112 cm. Find the length of its each side.

Q.

In given figure if AC = BC, $\angle$DCA = $\angle$ECB and $\angle$DBC = $\angle$EAC, then DC = __.

Q. PQRS is a parallelogram, in which PQ = 12 cm and its perimeter is 40 cm. Find the length of each side of the parallelogram.

Q.

If area of a ||gm with sides a and it is A and that of a rectangle with sides a and b is B then

(a) A > B

(b) A = B

(c) A < B

(d) $A\ge B$

Q.

A diagonal of a quadrilateral is a line segment that joins two __________ vertices of the quadrilateral.

Q.

In a parallelogram ABCD, if ∠A = 75^o, then ∠B =?

1. 15^o

2. 95^o

3. 105^o

4. 80^o

Q.

Q.

$ABCD$ is a trapezium in which $AB\parallel CD$ and $AD=BC$ show that
I) $\angle A=\angle B$
II) $\angle C=\angle D$
III) triangle $ABC$ congruent to triangle $BAD$
IV) diagonal $AC$ =diagonal $BD$
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Q.

The perimeter of a parallelogram is 32cm. If longer side measure 9.5cm, what is the measure of the shorter side.

Q.

Points $P$ and $Q$ have been taken on opposite sides $AB$ and $CD$, respectively of a parallelogram $ABCD$ such that $AP=CQ$. Show that $AC$ and $PQ$ bisect each other.

Q.

In the adjoining figure, $ABCD$ is a parallelogram. If $P$ and $Q$ are points on $AD$ and $BC$ respectively such that $AP=\frac{1}{3}AD$ and $CQ=\frac{1}{3}BC$, prove that $AQCP$ is a parallelogram.

Q.

If one pair of opposite sides are equal and parallel, then the figure is _____________.

Q.

In the given figure AD is the bisector of $\angle$A and AB = AC. Then $△$ACD and $△$ADB are congruent by which criterion?

1. SSS

2. SAS

3. ASA

4. None of these

Q. If the lengths of three sides of an isosceles trapezium are 10 cm, 5 cm and 4 cm, its perimeter CANNOT be

1. 23 cm
2. 25 cm
3. 29 cm
4. 31 cm

Q. Question 5
In figure AB and CD are common tangents to two circles of unequal radii prove that AB=CD

Q.

Q.

ABCD is a parallelogram in which AB = 9.5 cm and its perimeter is 30 cm. Find the length of each side of the parallelogram.

Q.

All rectangles are squares.

1. True
2. False

Q.

All the sides of a parallelogram are of equal length.

1. True
2. False

Q.

In the adjoining figure, $ABCD$ is a ||gm in which $E$ and $F$ are the midpoints of $AB$ and $CD$ respectively. If $GH$ is a line segment that cuts $AD,EF$ and $BC$ at $G,P$and $H$ respectively, prove that $GP=PH$.

Q. Diagonals of a parallelogram WXYZ intersect each other at point O. If $\angle$XYZ = ${135}^{°}$ then what is the measure of $\angle$XWZ and $\angle$YZW ?
If l(OY)= 5 cm then l(WY)= ?

Q.

In a parallelogram ABCD, points M and N have been taken on opposite sides AB and CD respectively such that AM = CN. Show that AC and MN bisect each other.