Theorem 2: Opposite Sides in a Parallelogram Are Equal

Q.

Prove that if a diagonal of a quadrilateral bisect each other, it is a parallelogram.

Q. Question 10
In figure, P is the mid-point of side BC of a parallelogram ABCD such that $\angle BAP=\angle DAP$. Prove that AD = 2CD .

Thinking process

Firstly, use the property that sum of cointeritor angles is ${180}^{\circ }$.Secondly use the property that sum of all angles in a triangle Is ${180}^{\circ }$ and then prove the required result.

Q. Find the value of $x$, if $ABCD$ is a parallelogram.

1. 2
2. 3
3. 4
4. 5

Q. In $\Delta ABC,\angle A={45}^{\circ },\angle B={60}^{\circ }$ and $\angle C={75}^{\circ }$. The angles of the triangle formed by joining the mid – points of the sides of this triangles are:

1. 
2. 
3. 
4. 

Q. Find the value of $x$, if $ABCD$ is a parallelogram.

1. 2
2. 5
3. 4
4. 3

Q. Find the value of $y$ if $ABCD$ is a parallelogram.

1. 7
2. 6
3. 2
4. 5

Q. For a parallelogram PQRS, PQ=8cm and QR= 4cm. Then PS=

1. 8cm
2. 4cm
3. 6cm

Q. Find the value of $xy$, if $ABCD$ is a parallelogram.

1. 6
2. 8
3. 9
4. 12

Q.

A quadrilateral is a parallelogram, if pair of opposite sides are equal and __.

Q.

Match the theorems and its properties:

1. A, B, C
2. A, A, A
3. A, A, B
4. A, B, B

Q. Find the value of $xy$, if $ABCD$ is a parallelogram.

1. 12

Q.

1. A, A, B
2. A, B, C
3. A, A, A
4. A, B, B

Q. Find the value of $x+y$, if $ABCD$ is a parallelogram.

1. 7

Q.

What is the necessary condition for a quadrilateral to be a parallelogram?

1. Only one pair of opposite sides are to be parallel.

2. Adjacent sides are equal.
3. It's opposite sides are equal and parallel.
4. The diagonals bisect each other at ${90}^{\circ }$

Q. The bisectors of angles $B$ and $C$ of a parallelogram $ABCD$ meet at point $O.$ If the triangle $OBC$ formed is an isosceles right triangle, then $ABCD$ is a rectangle.
If the above statement is true then mention the answer as $1,$ else mention $0$ if false.

Q. Find the value of $xy$, if $ABCD$ is a parallelogram.

1. 12

Q. Find the value of $xy$, if $ABCD$ is a parallelogram.

1. 12

Q. The ratio of two sides of a parallelogram is 3 : 5 and its perimeter is 48 m, then the sides of the parallelogram are

1. 9 m, 15 m
2. 5 m, 10 m
3. 4 m, 8 m
4. 9 m, 14 m

Q.

A quadrilateral can be divided into two congruent triangles. If the opposite sides are non-parallel, the quadrilateral is called ___.

1. Rhombus

2. Rectangle

3. Square

4. Kite

Q.

In the given figure, ABCD is a parallelogram. E is a point on DC. If AE bisects $\angle$A and BE bisects $\angle$B, then which of the following statements is correct?

1. AB = 12BC

2. AB = 3 B

3. AB = BC

4. AB = 2 BC

Q.

The quadrilateral formed by joining the mid-points of consecutive sides of a rectangle ABCD, taken in order, is a rhombus.

1. PQRS is a parallelogram

2. diagonals of PQRS are perpendicular and bisect each other

3. diagonals of PQRS are equal and bisect each other

4. PQRS is a rectangle

Q.

If BDEF and FDCE are parallelograms, then

___ lies equidistant to points B and C. (Fill in one among A/F/E/D).

Q. Opposite sides of a parallelogram are parallel, but not equal.

1. False
2. True

Q. Which of the following is correct for a parallelogram?

1. Diagonals are equal.
2. All sides are equal.
3. Adjacent angles are equal.
4. Adjacent angles are supplementary.

Q. Let $ABCD$ be a parallelogram and $\overrightarrow{AC},\overrightarrow{BD}$ are its diagonals Then, $\overrightarrow{AC}-\overrightarrow{BD}$ is

1. $3\overrightarrow{AB}$
2. $2\overrightarrow{AB}$
3. $3\overrightarrow{BC}$
4. $2\overrightarrow{BC}$

Q. Through A, B and C lines RQ, PR and QP have been drawn, respectively parallel to sides BC, CA and AB of a $\Delta ABC$ as shown in figure. Show that $BC=\frac{1}{2}QR$.

Q. Through A, B and C lines RQ, PR and QP have been drawn, respectively parallel to sides BC, CA and AB of a $\Delta ABC$ as shown in figure. Show that $BC=\frac{1}{2}QR$.