Opposite Sides in a Parallelogram Are Equal

Q.

Given a parallelogram ABCD. Complete each statement along with the definition or property used.

(i) AD = …

(ii) ∠DCB = …

(iii) OC = …

(iv) m∠DAB + m∠CDA = …

Q.

A square is a parallelogram where diagonals bisect each other to form ___.

1. right-angled triangles

2. isosceles triangle with two angles of ${60}^{\circ }$

3. scalene triangles

4. equilateral triangles

Q.

Define a parallelogram.

Q.

If in a quadrilateral ABCD, AB=BC and CD=DA and AB not equal to CD, then the figure formed would be a kite.

1. False

2. True

Q. Referring the adjacent figure of a parallelogram, write the answer of questions given below.

(1) If l(WZ) = 4.5 cm then l(XY) = ?
(2) If l(YZ) = 8.2 cm then l(XW) = ?
(3) If l(OX) = 2.5 cm then l(OZ) = ?
(4) If l(WO) = 3.3 cm then l(WY) = ?
(5) If m∠WZY = 120$°$ then m∠WXY = ? and m∠XWZ = ?

Q.

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

1. A diagonal divides it into two congruent triangles

2. It has opposite sides parallel

3. It has adjacent sides equal
4. The diagonals bisect each other at

Q.

Prove that a parallelogram inscribed in a circle is a rectangle. [2 MARKS]

Q.

what are the properties of parallelogram?

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 = BC

2. AB = 12BC

3. AB = 3 B

4. AB = 2 BC

Q.

If BDEF and FDCE are parallelograms, then "D" lies equidistant to points B and C.

1. True

2. False

Q.

In parallelogram ABCD, ∠A = 3 times ∠B. Find all the angles of the parallelogram. In the same parallelogram, if AB = 5𝒙 - 7 and CD = 3𝒙 + 1; find the length of CD.


[4 marks]

Q.

If BDEF and FDCE are parallelograms, then

___

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

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

Q.

In the given figure, AD = DC, AB = CB and if ∠A and ∠C are ${90}^{\circ }$ respectively, then, the figure is a parallelogram.

1. True

2. False

Q. $EFGH$ is a rhombus. Show that $EG$ bisects $\angle E$ and $\angle G$ both.

Q.

ABC is a right-angled triangle and O is the mid point of the side opposite to the right angle. Explain why O is equidistant from A, B and C. (The dotted lines are drawn additionally to help you).

Q. In the given figure, AP is bisector of $\angle A$ and CQ is bisector of $\angle C$ of parallelogram ABCD.
Prove that APCQ is a parallelogram

Q. State 'true' or 'false':

1. True
2. False

Q.

If the diagonal BD of a parallelogram bisects $\angle$B and $\angle$D, then ABCD is a

1. Rectangle

2. Rhombus

3. Square

4. Trapezium

Q.

Suppose in a quadrilateral ABCD, AC = BD and AD = BC. Prove that ABCD is a trapezium.

Q.

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

1. Square

2. Rectangle

3. Kite

4. Rhombus

Q.

Square, rectangle and rhombus are all parallelograms.

1. True

2. False

Q.

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