Quadrilaterals Class-6 RS Aggarwal ICSE Maths Goyal Brothers Prakashan

Quadrilaterals Class-6 RS Aggarwal ICSE Maths Goyal Brothers Prakashan Chapter-17 Solutions. We provide step by step Solutions of Exercise / lesson-17 Quadrilaterals for  ICSE Class-6  RS  Aggarwal  Mathematics.

Our Solutions contain all type Questions with Exe-17 to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-6 Mathematics

Quadrilaterals Class-6 RS Aggarwal ICSE Maths Goyal Brothers Prakashan Chapter-17 Solutions

–: Select Topics :–

Notes on Quadrilaterals

Exe-17

Quadrilateral Definition

A quadrilateral is a plane figure made with four Straight line segments closing in a space

A quadrilateral is a 4-sided Closed plane figure. 

• Every quadrilateral has 4 vertices, 4 angles, and 4 sides
• The total of its interior angles = 360 degrees

Types of Quadrilaterals

There are many types of quadrilaterals. As the word ‘Quad’ means four, all these types of a quadrilateral have four sides, and the sum of angles of these shapes is 360 degrees.

• Trapezium
• Parallelogram
• Squares
• Rectangle
• Rhombus
• Kite

Square Properties

• All the sides of the square are of equal measure
• The sides are parallel to each other
• All the interior angles of a square are at 90 degrees (i.e., right angle)
• The diagonals of a square perpendicular bisect each other

Rectangle Properties

• The opposite sides of a rectangle are of equal length
• The opposite sides are parallel to each other
• All the interior angles of a rectangle are at 90 degrees.
• The diagonals of a rectangle bisect each other.

Rhombus Properties

• All the four sides of a rhombus are of the same measure
• The opposite sides of the rhombus are parallel to each other
•  opposite angles are of the same measure
• The sum of any two adjacent angles of a rhombus is equal to 180 degrees
•  diagonals perpendicularly bisect each other

Parallelogram Properties

• The opposite side of the parallelogram are of the same length
•  opposite sides are parallel to each other
• The diagonals of a parallelogram bisect each other
•  opposite angles are of equal measure
• The sum of two adjacent angles of a parallelogram is equal to 180 degrees

Properties of Trapezium

• Only one pair of the opposite side of a trapezium is parallel to each other
• The two adjacent sides of a trapezium are supplementary (180 degrees)
•  diagonals of a trapezium bisect each other in the same ratio

Properties of Kite

•  pair of adjacent sides of a kite are of the same length
• The largest diagonal of a kite bisect the smallest diagonal
• Only one pair of opposite angles are of the same measure.

Exe-17 Quadrilaterals

 Class-6 RS Aggarwal ICSE Maths Goyal Brothers Prakashan

Page 221-222

Question 1:

Is the figure shown here a quadrilateral ? State, giving reason.

Answer :

No.

The reason is : A quadrilateral has bounded by four line  segments.

Question 2:

In the adjoining figure, PQRS is a quadrilateral.

(i) Name a pair of its adjacent sides.

(ii) Name a pair of its opposite sides.

(iii) Name a pair of its adjacent angles.

(iv) Name a pair of its opposite angles.

(v) Name its diagonals.

Answer :

(i) The adjacent  sides are :

PQ and PS

(ii) The opposite sides are :

PQ and RS

(iii) The adjacent angle are :

∠P and ∠Q

(iv) Name a pair of its opposite angles.

∠P and ∠R

(v) Name its diagonals.

PR and SQ

Question 3:

(i) How many pairs of adjacent sides does a quadrilateral have ?

(ii) How many pairs of opposite sides does a quadrilateral have ?

(iii) How many pairs of adjacent angles docs a quadrilateral have ?

(iv) How many pairs of opposite angles does a quadrilateral have?

(v)How many diagonals does a quadrilateral have ?

Answer :

(i) (AB, BC), (BC, CD), (CD, DA) and (DA, AB) are four pairs of adjacent sides of the quadrilateral ABCD.

(ii) (AB, CD) and (AD, BC) are two pairs of opposite sides of the quadrilateral ABCD.

(iii) (∠A, ∠C) and (∠B, ∠D) are two pairs of opposite angles of the quadrilateral ABCD.

(iv) (∠A, ∠B), (∠B, ∠C), (∠C, ∠D) and (∠D, ∠A) are four pairs of adjacent angles of the quadrilateral ABCD.

(v) AC and BD are the two diagonals of the quadrilateral ABCD.

Question 4:

For each of the statements given below, indicate whether it is true or false :

(i) A rectangle is a parallelogram.

(ii) A trapezium is a parallelogram.

(iii) A parallelogram is a trapezium.

(iv) A square is a rectangle.

(v) A square is a rhombus.

(vi) A rhombus is a square.

(vii) A parallelogram is a rhombus.

(viii) A kite is a parallelogram.

Answer :

(i) True

(ii) False

(iii) True

(iv) True

(v) True

(vi) False

(vii) False

(viii) False

Question 5:

In the adjoining figure, L and M are points on the sides PQ and PR respectively, of APQR such that LM || QR. What special name would you give to the quadrilateral
LQRM?

Answer :

Trapezium.

Question 6:

Let ABCD be a parallelogram. What special name would you give it, when :

(i) AB = AD ?
(ii) ∠ABC = 90°
(iii) AB = AD and ∠ABC=90° ?

Answer :

In a || gm ABCD
(i) AB  = AD,

then ABCD is a rhombus
(ii) ∠ABC = 90°
Then, ABCD is a rectangle.
(iii) AB = AD and ∠ABC = 90°,

 then ABCD is square.

Question 7:

(i) How does a trapezium differ from a parallelogram ?

(ii) How does a rhombus differ from a square ?

(iii) How does a kite differ from a parallelogram?

Answer :

(i) A quadrilateral having one and only one pair of opposite sides parallel is called a trapezium while a quadrilateral in which both pair of opposite sides are parallel, is called a parallelogram.

(ii) A parallelogram in which all sides are equal is called a rhombus while a parallelogram in which all the sides are equal and each angle is a right angle is called a square.

(iii) A quadrilateral which has two pairs of equal adjacent sides but unequal, opposite sides is called a kite while a quadrilateral in which both pairs of opposite sides are parallel, is called a parallelogram.

Question 8:

Answer :
ABCD is a parallelogram in which AB : BC = 5 : 3

–: End of Quadrilaterals Class-6 RS Aggarwal Solutions :–

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