example-1Multiple choice
Which of the following letters does not have any line of symmetry?
- (A)E
- (B)T
- (C)N
- (D)X
Show solution
Solution: Correct answer is (C) 11.4.2018
Chapter 9
Class 6 Mathematics · 88 questions · 0 with answers
Solved examples
example-2Multiple choice
Which of the following angles cannot be constructed using ruler and compasses?
- (A)75°
- (B)15°
- (C)135°
- (D)85°
Show solution
Solution: Correct answer is (D) In examples 3 to 5, fill in the blanks so that the statements are true:
example-3Fill in the blanks
If B is the image of A in line l and D is the image of C in line l, then AC = _________.
Show solution
Solution: BD
example-4Fill in the blanks
In Fig. 9.1, the line segments A B PQ and RQ have been D marked on a line l such that l PQ = AB and RQ = CD. P R Q Then AB – CD =__________. Fig. 9.1
Show solution
Solution: PR
example-5Fill in the blanks
The number of scales in a protractor for measuring the angles is __________.
Show solution
Solution: Two In examples 6 and 7, state whether the statements are true or false:
example-6Short answer
Using the set squares 30° – 60° – 90° and 45° – 45° – 90°, we can draw an angle of 75°.
Show solution
Solution: True. (Since 75° = 45° + 30° )
example-7Short answer
A circle has only 8 lines of symmetry.
Show solution
Solution: False (A circle has infinitely many lines of symmetry).
example-8Short answer
Write the letters of the word ALGEBRA which have no line of symmetry.
Show solution
Solution: The letters L, G and R have no line of symmetry. (Do you see why the dotted line is not the line of symmetry in ?) 11.4.2018
example-9Short answer
Draw a line segment equal to the sum of B two line segments given in Fig. 9.2 C D
Show solution
Solution: 1. Draw a line l and on it, cut a line segment Fig. 9.2 PQ = AB, using compasses. ( Fig. 9.3 ) P Q
example-10Short answer
Draw an angle equal to the difference of two angles given in Fig. 9.5. E F R Q Fig. 9.5
Show solution
Solution: 1. Draw an angle ABC equal to ∠DEF (as ∠DEF > ∠PQR), using ruler and compasses. 2. With BC as one of the arms, draw an angle SBC equal to ∠PQR such that BS is in the interior of ∠ABC as shown in Fig. 9.6. Then, ∠ABS is the required angle which is equal to ∠DEF – ∠PQR. B C [Note: For making ∠ABS = ∠DEF – Fig. 9.6 ∠PQR, how will you draw ray BS?] 11.4.2018
example-11Short answer
Complete Fig. 9.7 so that l is the line of symmetry of the completed figure. Fig. 9.7
Show solution
Solution: The figure can be completed as shown in Fig. 9.8, by drawing the points symmetric to different corners(points) with respect to line l. Fig. 9.8 In questions 1 to 17, out of the given four options, only one is correct. Write the correct answer. 1. In the following figures, the figure that is not symmetric with respect to any line is: (i) (ii) (iii) (iv) (A) (i) (B) (ii) (C) (iii) (D) (iv) 2. The number of lines of symmetry in a scalene triangle is (A) 0 (B) 1 (C) 2 (D) 3 11.4.2018 MATHEMATICS
Questions
Q2Short answer
With Q as centre and CD Fig. 9.3 as radius, draw an arc to cut a line segment QS = CD l P Q S on l as shown in Fig. 9.4. Then, line segment Fig. 9.4 PS is equal to the sum of AB and CD, i.e., PS = AB + CD
This question refers to a figure in the original PDF.
Q3Multiple choice
The number of lines of symmetry in a circle is
- (A)0
- (B)2
- (C)4
- (D)more than 4
Q4Multiple choice
Which of the following letters does not have the vertical line of symmetry?
- (A)M
- (B)H
- (C)E
- (D)V
Q5Multiple choice
Which of the following letters have both horizontal and vertical lines of symmetry?
- (A)X
- (B)E
- (C)M
- (D)K
Q6Multiple choice
Which of the following letters does not have any line of symmetry?
- (A)M
- (B)S
- (C)K
- (D)H
Q7Multiple choice
Which of the following letters has only one line of symmetry?
- (A)H
- (B)X
- (C)Z
- (D)T
Q8Multiple choice
The instrument to measure an angle is a
- (A)Ruler
- (B)Protractor
- (C)Divider
- (D)Compasses
Q9Multiple choice
The instrument to draw a circle is
- (A)Ruler
- (B)Protractor
- (C)Divider
- (D)Compasses
Q10Multiple choice
Number of set squares in the geometry box is
- (A)0
- (B)1
- (C)2
- (D)3
Q11Multiple choice
The number of lines of symmetry in a ruler is
- (A)0
- (B)1
- (C)2
- (D)4
Q12Multiple choice
The number of lines of symmetry in a divider is
- (A)0
- (B)1
- (C)2
- (D)3
Q13Multiple choice
The number of lines of symmetry in compasses is
- (A)0
- (B)1
- (C)2
- (D)3
Q14Multiple choice
The number of lines of symmetry in a protractor is
- (A)0
- (B)1
- (C)2
- (D)more than 2 SYMMETRY AND PRACTICAL GEOMETRY 137 11.4.2018
Q15Multiple choice
The number of lines of symmetry in a 45o - 45o - 90o set-square is
- (A)0
- (B)1
- (C)2
- (D)3
Q16Multiple choice
The number of lines of symmetry in a 30o - 60o - 90o set square is
- (A)0
- (B)1
- (C)2
- (D)3
Q17Multiple choice
The instrument in the geometry box having the shape of a triangle is called a
- (A)Protractor
- (B)Compasses
- (C)Divider
- (D)Set-square In questions 18 to 42, fill in the blanks to make the statements true.
Q18Fill in the blanks
The distance of the image of a point (or an object) from the line of symmetry (mirror) is ________ as that of the point (object) from the line (mirror).
Q19Fill in the blanks
The number of lines of symmetry in a picture of Taj Mahal is _______.
Q20Fill in the blanks
The number of lines of symmetry in a rectangle and a rhombus are ______ (equal/unequal).
Q21Fill in the blanks
The number of lines of symmetry in a rectangle and a square are______ (equal/unequal).
Q22Fill in the blanks
If a line segment of length 5cm is reflected in a line of symmetry (mirror), then its reflection (image) is a ______ of length _______.
Q23Fill in the blanks
If an angle of measure 80o is reflected in a line of symmetry, then the reflection is an ______ of measure _______.
Q24Fill in the blanks
The image of a point lying on a line l with respect to the line of symmetry l lies on _______.
Q25Fill in the blanks
In Fig. 9.10, if B is the image of the point A with A respect to the line l and P is any point lying on P l, then the lengths of line segments PA and PB are _______. B Fig. 9.10 11.4.2018
This question refers to a figure in the original PDF.
Q26Fill in the blanks
The number of lines of symmetry in Fig. 9.11 is__________. Fig. 9.11
This question refers to a figure in the original PDF.
Q27Fill in the blanks
The common properties in the two set-squares of a geometry box are that they have a __________ angle and they are of the shape of a __________.
Q28Fill in the blanks
The digits having only two lines of symmetry are_________ and __________.
Q29Fill in the blanks
The digit having only one line of symmetry is __________.
Q30Fill in the blanks
The number of digits having no line of symmetry is_________.
Q31Fill in the blanks
The number of capital letters of the English alphabets having only vertical line of symmetry is________.
Q32Fill in the blanks
The number of capital letters of the English alphabets having only horizontal line of symmetry is________.
Q33Fill in the blanks
The number of capital letters of the English alphabets having both horizontal and vertical lines of symmetry is________.
Q34Fill in the blanks
The number of capital letters of the English alphabets having no line of symmetry is__________.
Q35Fill in the blanks
The line of symmetry of a line segment is the ________ bisector of the line segment.
Q36Fill in the blanks
The number of lines of symmetry in a regular hexagon is __________.
Q37Fill in the blanks
The number of lines of symmetry in a regular polygon of n sides is_______.
Q38Fill in the blanks
A protractor has __________ line/lines of symmetry. 11.4.2018 UNIT-9
Q39Fill in the blanks
A 30o - 60o - 90o set-square has ________ line/lines of symmetry.
Q40Fill in the blanks
A 45o - 45o - 90o set-square has _______ line/lines of symmetry.
Q41Fill in the blanks
A rhombus is symmetrical about _________.
Q42Fill in the blanks
A rectangle is symmetrical about the lines joining the _________ of the opposite sides. In questions 43 - 61, state whether the statements are true (T) or false (F).
Q43Short answer
A right triangle can have at most one line of symmetry.
Q44Short answer
A kite has two lines of symmetry.
Q45Short answer
A parallelogram has no line of symmetry.
Q46Short answer
If an isosceles triangle has more than one line of symmetry, then it need not be an equilateral triangle.
Q47Short answer
If a rectangle has more than two lines of symmetry, then it must be a square.
Q48Short answer
With ruler and compasses, we can bisect any given line segment.
Q49Short answer
Only one perpendicular bisector can be drawn to a given line segment.
Q50Short answer
Two perpendiculars can be drawn to a given line from a point not lying on it.
Q51Short answer
With a given centre and a given radius, only one circle can be drawn.
Q52Short answer
Using only the two set-squares of the geometry box, an angle of 40o can be drawn.
Q53Short answer
Using only the two set-squares of the geometry box, an angle of 15o can be drawn.
Q54Short answer
If an isosceles triangle has more than one line of symmetry, then it must be an equilateral triangle.
Q55Short answer
A square and a rectangle have the same number of lines of symmetry.
Q56Short answer
A circle has only 16 lines of symmetry.
Q57Short answer
A 45o - 45o - 90o set-square and a protractor have the same number of lines of symmetry. 11.4.2018
Q58Short answer
It is possible to draw two bisectors of a given angle.
Q59Short answer
A regular octagon has 10 lines of symmetry.
Q60Short answer
Infinitely many perpendiculars can be drawn to a given ray.
Q61Short answer
Infinitely many perpendicular bisectors can be drawn to a given ray.
Q62Short answer
Is there any line of symmetry in the Fig. 9.12? If yes, draw all the lines of symmetry. B D Fig. 9.12
This question refers to a figure in the original PDF.
Q63Short answer
In Fig. 9.13, PQRS is a rectangle. State the lines of symmetry of the rectangle. P A Q S C R Fig. 9.13 11.4.2018
This question refers to a figure in the original PDF.
Q64Short answer
Write all the capital letters of the English alphabets which have more than one lines of symmetry.
Q65Short answer
Write the letters of the word ‘MATHEMATICS’ which have no line of symmetry.
Q66Short answer
Write the number of lines of symmetry in each letter of the word ‘SYMMETRY’.
Q67Multiple choice
Match the following: Shape Number of lines of symmetry (i) Isosceles triangle
- (a)6 (ii) Square
- (b)5 (iii) Kite
- (c)4 (iv) Equilateral triangle
- (d)3 (v) Rectangle (e) 2 (vi) Regular hexagon (f) 1 (vii) Scalene triangle (g) 0
Q68Multiple choice
Open your geometry box. There are some drawing tools. Observe them and complete the following table: Name of the tool Number of lines of symmetry
- (i)The Ruler _______
- (ii)The Divider _______
- (iii)The Compasses _______
- (iv)The Protactor _______ (v) Triangular piece with two equal sides _______ (vi) Triangular piece with unequal sides _______ 11.4.2018
Q69Short answer
Draw the images of points A and B in line l of l Fig. 9.14 and name them as A′ and B′ A respectively. Measure AB and A′ B′. Are they equal? Fig. 9.14
This question refers to a figure in the original PDF.
Q70Multiple choice
In Fig. 9.15, the point C is the image of point A in line l and line segment BC intersects the line l at P. A
This question refers to a figure in the original PDF.
- (a)Is the image of P in line l the point P itself?
- (b)Is PA = PC? P
- (c)Is PA + PB = PC + PB?
- (d)Is P that point on line l from which the Fig. 9.15 sum of the distances of points A and B is minimum?
Q71Short answer
Complete the figure so that line l becomes the line of symmetry of the whole figure (Fig. 9.16). Fig. 9.16
This question refers to a figure in the original PDF.
Q72Short answer
Draw the images of the points A, B and C in the line m (Fig. 9.17). Name them as A′, B′ and C′, respectively and join them in pairs. Measure AB, BC, CA, A′B′, B′C′ and C′A′. Is AB = A′B′, BC = B′C′ and CA = C′A′? B C Fig. 9.17 11.4.2018
This question refers to a figure in the original PDF.
Q73Short answer
Draw the images P′, Q′ and R′ of the points P, n Q and R, respectively in the line n (Fig. 9.18). P Join P′ Q′ and Q′ R′ to form an angle P′ Q′ R′. Measure ∠PQR and ∠P′Q′R′. Are the two angles equal? Q Fig. 9.18
This question refers to a figure in the original PDF.
Q74Short answer
Complete Fig. 9.19 by taking l as the line of symmetry of the whole figure. Fig. 9.19
This question refers to a figure in the original PDF.
Q75Short answer
Draw a line segment of length 7cm. Draw its perpendicular bisector, using ruler and compasses.
Q76Short answer
Draw a line segment of length 6.5cm and divide it into four equal parts, using ruler and compasses.
Q77Short answer
Draw an angle of 140o with the help of a protractor and bisect it using ruler and compasses.
Q78Short answer
Draw an angle of 65o and draw an angle equal to this angle, using ruler and compasses.
Q79Short answer
Draw an angle of 80o using a protractor and divide it into four equal parts, using ruler and compasses.Check your construction by measurement.
Q80Multiple choice
Copy Fig. 9.20 on your notebook and draw a perpendicular to l through P, using
This question refers to a figure in the original PDF.
- (i)set squares l
- (ii)Protractor
- (iii)ruler and compasses. How many Fig. 9.20 such perpendiculars are you able to draw? 11.4.2018
Q81Multiple choice
Copy Fig. 9.21 on your notebook and draw P a perpendicular from P to line m, using
This question refers to a figure in the original PDF.
- (i)set squares
- (ii)Protractor
- (iii)ruler and Fig. 9.21 compasses. How many such perpendiculars are you able to draw?
Q82Short answer
Draw a circle of radius 6cm using ruler and compasses. Draw one of its diameters. Draw the perpendicular bisector of this diameter. Does this perpendicular bisector contain another diameter of the circle?
Q83Short answer
Bisect ∠ XYZ of Fig. 9.22 Z X Fig. 9.22
This question refers to a figure in the original PDF.
Q84Short answer
Draw an angle of 60o using ruler and compasses and divide it into four equal parts. Measure each part.
Q85Short answer
Bisect a straight angle, using ruler and compasses. Measure each part.
Q86Short answer
Bisect a right angle, using ruler and compasses. Measure each part. Bisect each of these parts. What will be the measure of each of these parts?
Q87Short answer
Draw an angle ABC of measure 45o, using ruler and compasses. Now draw an angle DBA of O measure 30o, using ruler and compasses as 45O shown in Fig. 9.23. What is the measure of ∠DBC? B Fig. 9.23 C
This question refers to a figure in the original PDF.
Q88Short answer
Draw a line segment of length 6cm. Construct its perpendicular bisector. Measure the two parts of the line segment.
Q89Multiple choice
Draw a line segment of length 10cm. Divide it into four equal parts. Measure each of these parts. 11.4.2018 Activity 1: Make three different ink blot devils in your notebook and mark their line of symmetry. Activity 2: Draw all the lines of symmetry of Fig. 9.24 by paper folding. Fig. 9.24 Activity 3: Draw an angle of 15o by first drawing an angle of 60o and then an angle of 45o, using ruler and compasses. Activity 4: Using ruler and compasses D A draw an angle of 90o and in its interior, draw two rays with the O initial point of each as the vertex O of the angle so that each of the B 30 C three angles so formed is of 30o Fig. 9.25 (See Fig. 9.25). Activity 5: Draw an angle of 45o and in its interior, draw two rays to form three angles each of measure 15o, using ruler and compasses. Activity 6: Draw an angle of 135o and in its interior, draw two rays to form three angles each of equal measure, using ruler and compasses. A Activity 7: Draw the perpendicular bisectors of BC, CA and AB (Fig. 9.26). What do you B C observe? Fig. 9.26 Activity 8: Bisect AE and CE by drawing up their perpendicular bisectors in (Fig. 9.27). A D Let P be the point of intersection of these perpendicular bisectors check E whether B PA = PE, PE = PC Fig. 9.27 11.4.2018 Activity 9: Bisect BC and AB by drawing their B C perpendicular bisectors (Fig. 9.28). Make the point of intersecton as P. Check whether PA = PB = PC A D Fig. 9.28 Activity 10: Draw two line segments of lengths 8cm and 6cm. Using these line segments, construct a line segment of length (8 + 6)cm. Activity 11: Draw two line segments of lengths 3cm and 5cm. Construct line segments of the following lengths using these line segments:
This question refers to a figure in the original PDF.
- (a)6cm
- (b)15cm
- (c)(3+5)cm
- (d)(6+5)cm (e) (9 – 5)cm (f) (5 – 3)cm Activity 12: Draw two line segments of lengths 3cm and 6cm. Construct line segments, equal to the following lengths, using these line segments. 3+ 6 6 2( 3) + 6 (a) cm (b) cm (c) cm 2 2 2 Activity 13: Drop perpendiculars from D to AB and from D to AC (Fig. 9.29). B D C Fig. 9.29 C B Activity 14: O is the centre of the circle (Fig. 9.30). Drop perpendicular from B on CA. O Where does it meet CA? A Fig. 9.30 A D Activity 15: Copy the figure and bisect ∠A and ∠B (Fig. 9.31). Let the bisectors meet at some point P. Measure angle ∠APB. B C Fig. 9.31 11.4.2018 Activity 16: 1 3 Fig. 9.32 (a) Bisect angle 1 and angle 2 (Fig. 9.32). (b) Measure the angle between these bisectors. (c) Now bisect angle 3 and angle 4. (d) Measure the angle formed between these bisectors. (e) What do you obeserve from (b) and (d)? Can you conclude something? Activity 17: Construct an angle equal to 1 times the ∠PQR of Fig. 9.33, using ruler and compasses. Fig. 9.33 Activity 18: Bisect angle A, angle B and angle C (Fig. 9.34). What do you observe? B C Fig. 9.34 11.4.2018