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NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.3

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.3 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.3.

  • Understanding Quadrilaterals Class 8 Ex 3.1
  • Understanding Quadrilaterals Class 8 Ex 3.2
  • Understanding Quadrilaterals Class 8 Ex 3.4
Board CBSE
Textbook NCERT
Class Class 8
Subject Maths
Chapter Chapter 3
Chapter Name Understanding Quadrilaterals
Exercise Ex 3.3
Number of Questions Solved 12
Category NCERT Solutions

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.3

Ex 3.3 Class 8 Maths Question 1.
Given a parallelogram ABCD. Complete each statement along with the definition with the definiton or property used.
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals 15
(i)
AD = ………
(ii) ∠DCB = …………….
(iii) OC = ……………….
(iv) m∠DAB + m∠CDA = …………..
Solution.
(i) AD = BC : In a parallelogram, opposite sides are euqal.
(ii) ∠DCB = ∠DAB : In a parallelogram, opposite angles are equal.
(iii) OC = OA : The diagonals of a parallelogram bisect each other.
(iv) m∠DAB + m∠CDA = 180° : In a parallelogram, the stun of any two adjacent angles is 180°.

Ex 3.3 Class 8 Maths Question 2.
Consider the following parallelograms. Find the values of the unknowns x, y, z.
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals 16
Solution.
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals 17
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals 18
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals 19

Ex 3.3 Class 8 Maths Question 3.
Can a quadrilateral ABCD be a parallelogram if
(i) ∠D + ∠B = 180° ?
(ii) AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm
(iii) ∠A = 70° and ∠C = 65°?
Solution.
(i) If in a quadrilateral ABCD, ∠D + ∠B = 180°, then it is not necessary that ABCD is a parallelogram.
(ii) Since AD ≠ BC, i.e., the opposite sides are unequal, so ABCD is not a parallelogram.
(iii) Since ∠A ≠ ∠C, i.e., the opposite angles are unequal, so ABCD is not a parallelogram.

Ex 3.3 Class 8 Maths Question 4.
Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure.
Solution.
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals 20
A rough figure of a quadrilateral ABCD that is not a parallelogram has been drawn with exactly two opposite angles of equal measure such that ∠A – ∠C which is a kite as an example.

Ex 3.3 Class 8 Maths Question 5.
The measures of two adjacent angles of a parallelogram are in the ratio 3 :2. Find the measure of each of the angles of the parallelogram.
Solution.
Let two adjacent angles A and B of ||gm ABCD be 3x and 2x respectively.
Since the adjacent angles of a parallelogram are supplementary.
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals 21
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals 22
Since the opposite angles are equal in a parallelogram, therefore,
∠C = ∠A = 108° and ∠D = ∠B = 72°
Hence, ∠A = 108°, ∠B = 72°, ∠C = 108° and ∠D = 72°.

Ex 3.3 Class 8 Maths Question 6.
Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.
Solution.
Let two adjacent angles A and B of parallelogram ABCD be x each.
Since the adjacent angles of a parallelogram are supplementary.
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals 23

Ex 3.3 Class 8 Maths Question 7.
The adjacent figure HOPE is a parallelogram. Find the angle measures x, y and z. State the properties you use to find them.
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals 24
Solution.

Since HOPE is a parallelogram, therefore, HE || OP and HO || EP.
Now, HE || OP and transversal HO intersects them.
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals 25
Hence, x = 110°, y = 40° and z = 30°

Ex 3.3 Class 8 Maths Question 8.
The following figures GUNS and RUNS are parallelograms. Find x and y. (Lengths are in cm)
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals 26

Solution.
(i) Since GUNS is a parallelogram, therefore, its opposite sides are equal.
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals 27
(ii) In a parallelogram, diagonals bisect each other, therefore,
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals 28

Ex 3.3 Class 8 Maths Question 9.
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals 29
In the below figure both RISK and CLUE are parallelograms. Find the value of x.
Solution.
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals 30

Ex 3.3 Class 8 Maths Question 10.
Explain how this figure is a trapezium. Which of its two sides are parallel ?
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals 31
Solution.

Since ∠KLM + ∠NML = 180° i.e., the pair of consecutive interior angles are supplmentary.
Therefore, KL || NM and so KLMN is a trapezium.

Ex 3.3 Class 8 Maths Question 11.
Find m∠C in the figure, if \(\overline { AB } \) || \(\overline { DC } \).
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals 32
Solution.

Since AB || DC and transversal BC intersects
them.
∠B + ∠C= 180°
[∵ Sum of interior angles is 180°]
⇒ 120°+ ∠C =180° A
⇒ ∠C = 180°- 120° = 60°
Hence, m∠C =60°

Ex 3.3 Class 8 Maths Question 12.
Find the measure of ∠P and ∠S, if \(\overline { SP } \) || \(\overline { RQ } \) in the figure. (If you find mZ R, is there more than one method to find m∠P ?)
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals 33
Solution.

Since SP || RQ and PQ is a transversal intersecting them at P and Q.
∴ ∠P + ∠Q =180°
[∵ Sum of interior angles is 180°]
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals 34

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