Class – 8 Maths (Prachi Publication) chapter – 7 (Understanding Shapes)

In this article we will get the solution for all the assignments of Class 8 Maths Prachi Publication Chapter 7 Understanding Shapes.
In this chapter, we have been given the solution of Assignment 6.1, 6.2 and 6.3 in a simple and easy way by Study Circle.
Class 8 Maths Prachi Publication Chapter 7 Understanding Shapes and Exercises also contains solutions for Section A and Section B. These types of solutions provided by Study Circle will be very helpful for the students and will be of great help to them.

Class – 8 Maths (Prachi Publication) chapter – 7

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3 B. A pairs of opposite sidesC. A pairs of adjacent anglesD. A pairs opposite angles
3.2 ASSIGNMENT – 7.2

ASSIGNMENT 7.1

Question 1-  Three angles of a quadrilateral are 100°, 50° and 50° respectively Find the measure of fourth angle.​ 

(a) 140°           (b)   160°        (c)  120°       (d)   100°  

Solution:–

Class - 8 Maths (Prachi Publication) chapter - 6

 

 

(iii) The four angles of a quadrilateral are in the ratio 1: 3: 7: 9. which of the following is not the angle of this quadrilateral ? 

(a) 18 °          (b) 54 °           (c) 126°         (d)  108 °

Solution – By angle sum property , we get 

1x + 3x + 7x+ 9x = 180°

20x = 360°

x = 360/20

x = 18°

The angles of the

1x = 18°

3x = 54°

7x = 126°

9x = 162°

 Answer — Hence the only incorrect option is 108° (option d)

 

Q -2 Look at the adjoining figure of a ◻ABCD and name its following :

A. A pairs of adjacent sides

B. A pairs of opposite sides
C. A pairs of adjacent angles
D. A pairs opposite angles

Answer :– (A)  A Pair of adjacent angles are :-
AB , AD
BA , BC
CB , CD 
DA , DC
 
(B) — A Pair of opposite sides —
AB , CD 
BC , AD
 
(C) — A Pair of adjacent angles —
∠ A , ∠ B
∠ B ∠ C 
∠ C ∠ D
∠ D ∠ A
  
(D) — A Pair of opposite angles
∠ A ∠ C
∠ B ∠ D
 
Q -3 In the figure of Q. no 2, the two diagonals of the quadrilateral ABCD. 
Answer — Two diagonals of quadrilateral ABCD are: —
              AC and BD 
 
Q -4 Join Q and S in the adjoining figure and prove that :–
∠ P+ ∠ Q +∠ R +∠ S = 360°
Solution — In △ PQR 
∠ 1 + ∠ 2 + ∠ 6 = 180°   ——      (1)
In △ QRS
∠ 3 + ∠ 4 +∠ 5  = 180° ————(2)
Adding equation (1) and (2) we get 
∠ 1 + (∠ 2 + ∠ 3) + ∠ 4 + (∠ 5 + ∠ 6) = 180° +180° 
∠ P +∠ Q + ∠ R + ∠ S = 360°
Hence proved .
Q –5 The Three angles of a quadrilateral are equal . If the measure of the fourth angle is 120°, what is the measure of the equal angles .
Solution — Let the equal angles be x
    fourth angle = 120° 
 by angle sum property , we have 
   x + x + x + 120° = 360° 
3x + 120°  = 360 
3x = 360° – 120° 
3x = 240° 
x = 240 / 3
x = 80° 
Hence each angle are 80° each and fourth angle is 120° 
 
Q — 6 Two angles of a quadrilateral are of measure 75° each and the other two angle are equal. What is the measure of either of these two equal angles ? 
 
Answer:–
Class - 8 Maths (Prachi Publication) chapter - 7 (Understanding Shapes)

 

Q — 7 If three angles of a quadrilateral are 20° , 90° and 90° , find the fourth angle of the quadrilateral .                                                                                                               
 
Answer –7                                                                                                                                            
Class - 8 Maths (Prachi Publication) chapter - 7 (Understanding Shapes)
Question — 8 The measure of two adjacent angles of a quadrilateral are 85 and 115 and the other two angles are equal . Find the measure of each angles.    

Answer —             

Class - 8 Maths (Prachi Publication) chapter - 7 (Understanding Shapes)
 

Q –9 Four angles of a quadrilateral are 2: 3: 4: 1. Find the angles

 Answer — Given ratio = 2 : 3 : 4 : 1                                                    
let the measure of four angles = 2x , 3x , 4x , x by angle sum property
2x + 3x + 4x + x = 360° 
10x = 360°
x = 360 / 10 
x = 36°
2x = 2 ✖ 36 = 72°
3x = 3 ✖ 36 = 108°
4x = 4 ✖ 36 = 144 °
x = 36° 
 
       Q — 10 The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. What is the measure of the four angles separately ? 
Answer — Given ratio = 1: 2 : 3 : 4                                                    
 let the measure of four angles = x , 2x , 3x , 4x by angle sum property 
x + 2x + 3x + 4x = 360°
10x = 360° 
x = 360 / 10 
x = 36°
2x = 2 ✖ 36 = 72°
3x = 3 ✖ 36 = 108°
4x = 4 ✖ 36 = 144 °
 
Q — 11 The four angles of a quadrilateral are in the ratio 3 : 5 : 7 : 9. Find the angles of the quadrilateral.
 

Q –12 In the adjoining figure , E is a point in the interior of ∠ AOB , such that EC ⟂ OB and ED ⟂ OA. If  ∠ AOB = 36° ,what is the measure of ∠ CED ?

 

Q — 13 The sum of two angles of a quadrilateral is 150° and the other angles are in the ratio 2 : 3. Find the measure of each angle . 

 

 

Class – 8 Maths (Prachi Publication) chapter – 7 

                                        ASSIGNMENT – 7.2

Q – 1 Multiple Choice Questions (MCQ)

(i) Two adjacent sides of a parallelogram are 3cm and 4cm respectively. The perimeter of the parallelogram is
(a) 12cm (b) 13cm (c) 14cm (d) 15cm

Solution :–
Length of two adjacent sides = 4 cm and 3 cm i.e.,
l=4 cm and b = 3 cm
∴ Perimeter = 2(l+b)
= 2 ( 4 + 3 ) c m
= 2 × 7 = 14 c m

(ii) The long side of a parallelogram is 8cm. If the shorter side is 3/4 of the longer side, the perimeter of the parallelogram is
(a) 28cm (b) 26cm (c) 24cm (d) 22cm

Solution :- Length is 8cm
Breadth is 3/4 × 8 = 6cm
Therefore perimeter= 2(l+b) = 2(8+6)
= 21 × 4 = 28cm

(iii) In a parallelogram ABCD , ∠A = 45 ° , then the other angles are
(a) 145 ° , 45 ° , 145 °
 (b) 150 ° , 40 ° , 150 °
 (c) 135 ° , 45 ° ,135 °
(d) None of these

Solution:–

For a parallelogram ABCD,
∠A=∠C , ∠B=∠D
by angle sum property ∠A+∠B+∠C+∠D=360°
∠A= 45 ° (given)
∠C = 45 °
45 ° + ∠B + 45 ° + ∠D = 360°
90° + 2 ∠B = 360°
∠B=∠D=135°
Q –2 The longer side of a parallelogram is 8.4 cm and the shorter side is half of the longer side . Find the perimeter of the parallelogram.
Solution:–
Longer side = 8.4cm
Shorter side = 8.4/2 = 4.2 cm
Perimeter=2( l+b)
= 2 (8.4+4.2) = 25.2cm
Q–3 The ratio the adjacent sides of a parallelogram is as 2 : 3, and its perimeter is 40cm . Find the sides of the parallelogram.
Solution :–
Let adjacent sides of the parallelogram be 2x and 3x
Then , 2x + 3x + 2x + 3x = 10x
perimeter is given = 40cm
10x = 40cm
x = 40/10 = 4cm
2x = 2 × 4 = 8cm
3x = 3 × 4 = 12cm
Q–4 The ratio the adjacent sides of a parallelogram is as 2 : 3, and its perimeter is 60cm . Find the sides of the parallelogram.
Solution:–
Ratio = 2:3
Put x in the ratio,
Length (l) = 2x
Breadth (b) = 3x
Perimeter = 60 cm
Perimeter = 2( l + b )
2( 2x + 3x ) = 60 cm
2 × 5x = 6ocm
10x = 60cm
x = 60 /10
x = 6cm
The value of x is 6 cm
Length = 2x = 2×6 = 12 cm
Breadth = 3x = 3×6 = 18 cm

Q–5 The perimeter of a parallelogram is 150cm. One of its sides is greater than the other by 33cm. Find the lengths of the sides of the parallelogram.
Solution :–
let the breadth be = x cm
and length be = x +33 cm
Given perimeter = 150 cm
Perimeter = 2 ( l + b )
2 ( x + x + 33 ) = 150 cm
2 ( 2x + 33 ) = 150 cm
4x + 66 = 150 cm
4x = 150 – 66
4x = 84 cm
x = 84 / 4
x = 21 cm
breadth = 21 cm
length = 21 + 33 = 54 cm
Q–6 Two adjacent angles of a parallelogram are in the ratio 4:5 . Find the measure of all the angles.
Solution:–

The ratio between two adjacent angles of a || gm ABCD are in the ratio 4 : 5
Let ∠ A = 4 x
and ∠ B = 5 x
But ∠ A + ∠ B = 180°
⇒ 4 x + 5 x = 180°
⇒ 9 x = 180°
∴ x = 180 / 9 = 20°

Class - 8 Maths (Prachi Publication) chapter - 7 (Understanding Shapes)

∴ ∠ A = 4 x = 4 × 20° = 80 °
∠ B = 5 x = 5 × 20° = 100°
∠C = 4x = 4 × 20° = 80°
∠D = 5 x = 5 × 20° = 100°
Q–7 Two adjacent angles of a parallelogram are in the ration of 2:1. Find the measure of each angle.
Solution:–

Class - 8 Maths (Prachi Publication) chapter - 7 (Understanding Shapes)

Q –8  Two adjacent angles of a parallelogram are in the ration of 7:2. Find the measure of all the angles of parallelogram.
Solution:–
Q–9 In the adjoining Figure , ABCD is a parallelogram if ∠DAB = 85° and ∠DBA = 60°, then calculate:–
(i) ∠CDB (ii) ∠ABD
Solution–
(i) In parallelogram ABCD, ∠A = ∠C = 85°
. In ∆BCD,
∠DBC + ∠BCD + ∠CDB = 180°
i.e. 60° + 85° + ∠CDB = 180°
or 145° + ∠CDB = 180°
or ∠CDB = 180° – 145° = 35°
(ii) ABCD is a parallelogram,
so AB || DC, BD is a transversal.
∴ ∠ABD = ∠CDB [Alternate interior opp. angles]
i.e. ∠ABD = ∠CDB = 35°

Class – 8 Maths (Prachi Publication) chapter – 7

                                     ASSIGNMENT – 7.3 

Q – 1 Multiple choice Questions (MCQ) Choose the correct option .

(i) Which of the following is not correct for a rhombus ?

(a) Diagonals bisect each other. (b) All angles are 90°

(c) Diagonals perpendicular to each other (d) All sides equal.

Solution :– option b , All angles are 90°

(ii) If one of the angles formed by diagonals and adjacent sides of a rhombus is 20° , all four angles of the rhombus are

(a) 40° , 140° , 40° , 140° (b) 50° , 130° , 50° , 130°

(c) 60° , 120° , 60° , 120° (d) None of these.

Solution :–

Class - 8 Maths (Prachi Publication) chapter - 7 (Understanding Shapes)

 Option A , (a) 40° , 140° , 40° , 140° 

 

iii) If a perpendicular drawn from an obtuse – angled vertex of a rhombus to the opposite side bisects the side , all angles of the rhombus are :–

(a) 70°  , 110°  , 70°  , 110°                     (b)  40°  , 140°  , 40°  , 140°  

(c)  50°  , 130°  , 50°  , 130°                    (d) 60°  , 120°  , 60°  ,120°

Solution :–     

Class - 8 Maths (Prachi Publication) chapter - 7 (Understanding Shapes)

 

Q– 2 For each of the following statements , state whether the statement is true (T) or false (F) :-   Solution:–

(i) Every square is a rectangle. — True

(ii) Every parallelogram is a rhombus. —- False

(iii) Every rectangle is a parallelogram. —— True
(iv) Every rectangle is a square. ———– False
(v) Every square is a rhombus,———- True
(vi) Every rhombus is a square.————-False

(vii) Every square is a parallelogram. ——-True

(viii) Every rhombus is a parallelogram. —–True

(ix) Every parallelogram is a rectangle.———-False

(x) Every parallelogram is a trapezium.———-True
(xi) Every parallelogram is a square.————-False
(xii) Every square is a trapezium. —————-True
(xiii) Every trapezium is a square. —————–False
(xiv) Every trapezium is a parallelogram.​———False
Q–3 Which of the following statements are true (T) or false (F) for a rectangle and a square:–
(i) It has all its sides of equal length.
(ii) It has two pairs of opposite sides of equal length.
(iii) Its diagonals bisect each other.
(iv) Its diagonals are perpendicular and bisect each other.
(v) Its diagonals are equal and perpendicular to each other.
(vi) Its diagonals are perpendicular to each other.
(vii)) Its diagonals are equal , perpendicular and bisect each other.
(viii) All of its angles are equal.
(ix) Its diagonals are equal and bisect each other.
(x) Its diagonals are equal.
Solution:–
Rectangle
(i) F
(ii) T
(iii) T
(iv) F
(v) F
(vi) F
(vii) F
(viii) T
(ix) T
(x) T
 
Square:–
(i) T
(ii) T
(iii) T
(iv) T
(v) T
(vi) T
(vii) T
(viii) T
(ix) T
(x) T

 

 

 

Q – 4 Which of the following statements are (T) or (F) for a rhombus ?

Answer:–

 

(i) It has only two pairs of equal sides .–  F

 

(ii) It has two pairs of parallel sides………..T

 (iii) Two of its angles are at right angles….F
 (iv) It has two pair of parallel sides…………T
 (v) Its diagonals are equal and perpendicular to each other……….F
 (vi) It has all its sides of equal lengths………….T 
 (viii) Its diagonals bisect each other at right angle…………F
 
Q–5 ABCD is parallelogram. What special name will you give it, if the following additional facts are known ? 
(i)  AB = AD                 (ii) ∠DAB = 90°              (iii) AB = AD and ∠DAB = 90°
Solution:–
 
Class - 8 Maths (Prachi Publication) chapter - 7 (Understanding Shapes)

Q–6 In the adjoining figure , ABCD is a rhombus. 

find the measure of the following angles , if ∠ACB = 30°
(i)  ∠BOC                                   (ii)     ∠CBO 
( iii)   ∠OAD                                 (iv)    ∠ABO
Solution :–
 
Q — 7 In a given rectangle ABCD , diagonals AC and BD intersect at O . If ∠COD = 120° find  ∠ OBA . 
Solution :–

class - 8 Mathematics (prachi publication) chapter-7

Q – 8   In the given figure , prove that the diagonals of a rectangle are equal .
Solution :-– 
 

class 8 mathematics prachi publication chapter 7

Q — 9   Prove that diagonals of a rhombus bisect each other at right angles as given in the adjoining figure .   
Solution:–                                                                                               
                  

class - 8 Mathematics (prachi publication) chapter-7

 

 

Q– 10 Prove that a rhombus with one angle 90° is a square.
Solution:—

 class - 8 Mathematics (prachi publication) chapter-7

Q– 11 Show that the four triangles as shown in the adjoining figure formed by diagonals and sides of rhombus are congruent. 

Solution:–
 

. Diagonals of a rhombus bisect each other at right angles.

 In ∆s COD and BOC, we have
 DC = BC [Sides of rhombus] 

∠COD = ∠BOC [Each 90°]                                                              

 

OC = OC [Common]
 ∴ ∆CDO ≅ ∆BOC [By SAS] 
Similarly, we can prove that ∆BOC ≅ ∆AOB,
 ∆AOB ≅ ∆AOD,
 ∆AOD ≅ ∆COD.
 Thus, ∆COD ≅ ∆BOC ≅ ∆AOB ≅ ∆AOD.
 Hence, the four triangles are congruent. Hence proved.
 
Q–12 In the given figure , ABCD is a rectangle . BM and DN are perpendiculars to AC from B and D respectively. Prove that AN=CM.
Solution:—                                                                                         
 
Class - 8 Maths (Prachi Publication) chapter - 7 (Understanding Shapes)

 

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