- Quadrilateral
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- Parallelogram
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- Trapezium
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- Rhombus
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- Rectangle
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- Square
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- Mid-point Theorem for Triangles
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- How to solve the angle Problem in Quadilateral
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- Additional Topics

Given below are the **Class 9 Maths** Important Questions for Quadilaterals

b) Calculation problems

c) Multiple choice questions

d) Long answer questions

e) Fill in the blank's

**Question 1**

Which are these is true or false about parallelogram

- The diagonals of a parallelogram bisect each other
- In a parallelogram, opposite sides and angle are equal.
- A diagonal of a parallelogram divides it into two congruent triangles
- The bisectors of the angles of parallelogram create a rectangle
- Sum of all the internal angles is 360
^{0} - Sum of all the exterior angles is 180
^{0} - Square, rectangle and rhombus are all parallelogram
- Consecutive angles are supplementary

**Solution **

- True. It is by definition
- True. It is by definition
- True. This can be proved easily using SSS congruence
- True
- True. This can easily proved by drawing one diagonal and summing all the angles based on triangle angle sum
- False
- True
- True

**Question 2**

**True or False statement**

- All the angles of the quadrilateral are obtuse
- Diagonal of the rhombus are equal and perpendicular to each other
- Diagonal of the square are equal and bisect each other at right angle
- Out of four points A,B,C,D in place, there are collinear. A quadrilateral can be formed from these points
- Trapezium, in which the sides that are not parallel are equal in length and angles formed by parallel sides are equal, such trapezium is called isosceles trapezium
- In a parallelogram, diagonal bisect the angles

**Solution **

- False
- false
- True
- False
- True
- True

**Question 3**

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD

Which of the following is true based on given information

a) AP=CQ

b) QD=PB

c) DP=QB

d) ΔPAD≅ ΔQCB

**Solution**

All are correct

In Triangle ΔPAD and ΔQCB

AD=CB

Angle P= Angle Q=90^{0}

∠CBQ=∠ADP Alternate interior angles of AB||CD

So AAS congruence

Also as they are congruent, we get AP=CQ and DP=QB

Now Lets see the triangles ?APB and ?CQD

AB=CD

Angle P= Angle Q=90^{0}

Alternate interior angles of AB||CD

So QD=PB

**Question 4**

The angles of the quadrilateral are in the ratio 2:5:4:1?

Which of the following is true?

a) Largest angle in the quadrilateral is 150^{0}

b) Smallest angle is 30^{0}

c) The second largest angle in the quadrilateral is 80^{0}

d) None of these

**Solution **(a) and (b)

Angles are 2x, 5x,4x,x

Now

2x+5x+4x+x=360

Or x=30

Angles are 30, 60,120,150

**Question 5**

Two adjacent angles in a parallelogram are in the ration 2:4. Find the values?

a) 80,100

b) 40,140

c) 60,120

d) None of the above

**Solution** (c)

Adjacent angles

2x+4x=180

x=30

60,120 are adjacent angles

**Question 6**

ABCD is a trapezium with AB =10cm, AD=5 cm, BC=4 cm and DC =7 cm?

Find the area of the ABCD

a) 34 cm^{2}

b) 28cm^{2}

c) 20 cm^{2}

d) None of these

**Solution** (a)

BC is the altitude between the two parallel sides AB and DC

So Area of trapezium will be given by

A=(1/2)BC(AB+DC)=34cm^{2}

**Question 7**

PQRS is a quadrilateral whose diagonal bisect each other at right angles

a) PQRS is a Square

b) PQRS is a rectangle

c) PQRS is a rhombus

d) None of these

**Solution** (c)

**Question 8**

ABCD is a trapezium where AB||DC. BD is the diagonal and E is the mid point of AD. A line is draw from point E parallel to AB intersecting BC at F. Which of these is true?

a) BF=FC

b) EA=FB

c) CF=DE

d) None of these

**Solution** (a)

Let’s call the point of intersection at diagonal as G

Then in triangle DAB

EG||AB and E is the mid point of DA,So by converse of mid point theorem,

G is the mid point of BD

Now in triangle DBC

GF||CD

G is the mid point of DB

So by converse of mid point theorem

F is the mid point of BC

**Question 9**

ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively

a) PQRS is a rectangle

b) PQRS is a parallelogram

c) PQRS is a rhombus

d) None of these

**Solution** (c)

**Question 10**

In a parallelogram PQRS, The bisector of angles P and Q meet at point O as shown in below figure. What is the angle O?

a) 80

b) 90

c) 45

d) None of the above

**Solution** (b)

Rhombus |
Is a quadrilateral with only one pair of parallel sides. |

Rectangles |
Is a quadrilateral whose Two pairs of adjacent sides of a kite are equal, and one pair of opposite angles is equal. Diagonals intersect at right angles. One diagonal is bisected by the other. |

Kite |
Is a quadrilateral whose all the sides are equal and opposite sides are parallel. Opposite angles are equal. |

Right-angled trapezoid |
Is a quadrilateral whose opposite sides of a rectangle are parallel and equal. All angles are 90º. |

Isosceles trapezoid |
A trapezoid having two right angles |

Trapezoid |
Is a trapezoid whose non parallel sides are equal |

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