example-1Multiple choice
The number of diagonals of a pentagon is
- (A)3
- (B)4
- (C)5
- (D)10
Show solution
Solution: Correct answer is (C). 11.4.2018
Chapter 2
Class 6 Mathematics · 78 questions · 75 with answers
Solved examples
example-2Multiple choice
The number of diagonals of a triangle is
- (A)0
- (B)1
- (C)2
- (D)3
Show solution
Solution: Correct answer is (A). In examples 3 and 4, fill in the blanks to make the statements true:
example-3Fill in the blanks
A polygon of six sides is called a ______.
Show solution
Solution: Hexagon
example-4Fill in the blanks
A triangle with all its sides of unequal lengths is called a ______ triangle.
Show solution
Solution: Scalene In examples 5 to 7, state whether the statements are true or false.
example-5Short answer
Two non-parallel line segments will always intersect.
Show solution
Solution: False (Hint: They will intersect, when they are produced)
example-6Short answer
All equilateral triangles are isosceles also.
Show solution
Solution: True
example-7Short answer
Angle of 0° is an acute angle.
Show solution
Solution: False [Hint: Measure of acute angle is between 0° and 90°]
example-8Short answer
In Fig. 2.1, PQ ⊥ AB and PO = OQ. Is PQ the perpendicular bisector of P line segment AB? Why or why not?
Show solution
Solution: PQ is not the perpendicular A O B bisector of line segment AB, because AO ≠ BO. [Note: AB is the Q perpendicular bisector of line segment PQ]. Fig. 2.1
example-9Short answer
In Fig. 2.2, if AC ⊥ BD , then name all the right angles.
Show solution
Solution: There are four right angles. They are: ∠APD , ∠APB , ∠BPC and ∠CPD . Fig. 2.2 11.4.2018
example-10Short answer
Is ABCD of Fig. 2.3 a polygon? If yes, what is the special name for it?
Show solution
Solution: Yes, it is a polygon, because it is a simple closed figure made of line segments only. It is a quadrilateral. Fig. 2.3
example-11Multiple choice
In Fig. 2.4, BCDE is a square and a 3D shape has been formed by joining the point A in space with the vertices B, C, D and E. Name the 3D shape and also its
- (i)vertices,
- (ii)edges and
- (iii)faces.
Show solution
Solution: The 3D shape formed is a square pyramid. (i) Vertices are A, B, C, D and E. (ii) Edges are AB, AC, AD, AE, BC, CD, DE and EB. (iii) Faces are: square BCDE and triangles ABC, ACD, ADE and Fig. 2.4 ABE.
example-12Short answer
Write the measure of smaller angle formed by the hour and the minute hands of a clock at 7 O’ clock. Also, write the measure of the other angle and also state what types of angles these are.
Show solution
Solution : Measure of the required angle = 30° + 30° + 30° + 30° + 30° = 150° Measure of the other angle = 360° – 150° = 210° Angle of measure 150° is an obtuse angle and that of 210° is a reflex angle. In each of the questions 1 to 16, out of four options only one is correct. Write the correct answer.
Questions
Q1Multiple choice
Number of lines passing through five points such that no three of them are collinear is
- (A)10
- (B)5
- (C)20
- (D)8 11.4.2018
Show answer
(A) 10
Q2Multiple choice
The number of diagonals in a septagon is
- (A)21
- (B)42
- (C)7
- (D)14
Show answer
(D) 14
Q3Multiple choice
Number of line segments in Fig. 2.5 is
This question refers to a figure in the original PDF.
- (A)5
- (B)10
- (C)15
- (D)20 Fig. 2.5
Show answer
(B) 10
Q4Multiple choice
Measures of the two angles between hour and minute hands of a clock at 9 O’ clock are
- (A)60°, 300°
- (B)270°, 90°
- (C)75°, 285°
- (D)30°, 330°
Show answer
(B) 270°, 90°
Q5Multiple choice
If a bicycle wheel has 48 spokes, then the angle between a pair of two consecutive spokes is 1 1 2 2
- (A)5
- (B)7
- (C)
- (D)2 2 11 15
Show answer
(B) 7
Q6Multiple choice
In Fig. 2.6, ∠XYZ cannot be written as
This question refers to a figure in the original PDF.
- (A)∠Y
- (B)∠ZXY
- (C)∠ZYX
- (D)∠XYP Fig. 2.6
Show answer
(B) ∠ZXY
Q7Multiple choice
In Fig 2.7, if point A is shifted to point B along the ray PX such that PB = 2PA, then the measure of ∠BPY is A 45°
This question refers to a figure in the original PDF.
- (A)greater than 45°
- (B)45° P Y
- (C)less than 45°
- (D)90° Fig. 2.7
Show answer
(B) 45° P Y
Q8Multiple choice
The number of angles in Fig. 2.8 is 40°
This question refers to a figure in the original PDF.
- (A)3
- (B)4 20°
- (C)5
- (D)6 30° Fig. 2.8 11.4.2018
Show answer
(D) 6 30° Fig. 2.8 11.4.2018
Q9Multiple choice
The number of obtuse angles in Fig. 2.9 is
This question refers to a figure in the original PDF.
- (A)2
- (B)3
- (C)4
- (D)5 65° 45° 20° 30° Fig. 2.9
Show answer
(C) 4
Q10Multiple choice
The number of triangles in Fig. 2.10 is
This question refers to a figure in the original PDF.
- (A)10
- (B)12
- (C)13
- (D)14 Fig. 2.10
Show answer
(B) 12
Q11Multiple choice
If the sum of two angles is greater than 180°, then which of the following is not possible for the two angles?
- (A)One obtuse angle and one acute angle
- (B)One reflex angle and one acute angle
- (C)Two obtuse angles
- (D)Two right angles.
Show answer
(D) Two right angles.
Q12Multiple choice
If the sum of two angles is equal to an obtuse angle, then which of the following is not possible?
- (A)One obtuse angle and one acute angle.
- (B)One right angle and one acute angle.
- (C)Two acute angles.
- (D)Two right angles.
Show answer
(D) Two right angles.
Q13Multiple choice
A polygon has prime number of sides. Its number of sides is equal to the sum of the two least consecutive primes. The number of diagonals of the polygon is
- (A)4
- (B)5
- (C)7
- (D)10 11.4.2018
Show answer
(B) 5
Q14Multiple choice
In Fig. 2.11, AB = BC and AD = BD = DC. A The number of isoscles triangles in the figure is
This question refers to a figure in the original PDF.
- (A)1
- (B)2 D
- (C)3
- (D)4 B C Fig. 2.11
Show answer
(C) 3
Q15Multiple choice
In Fig. 2.12, A ∠BAC = 90° and AD ⊥ BC. The number of right triangles in the figure is
This question refers to a figure in the original PDF.
- (A)1
- (B)2 B D C
- (C)3
- (D)4 Fig. 2.12
Show answer
(C) 3
Q16Multiple choice
In Fig. 2.13, PQ ⊥ RQ, PQ = 5 cm and QR = 5 cm. Then ∆ PQR is
This question refers to a figure in the original PDF.
- (A)a right triangle but not isosceles
- (B)an isosceles right triangle 5
- (C)isosceles but not a right triangle
- (D)neither isosceles nor right triangle Q 5 R Fig. 2.13 In questions 17 to 31, fill in the blanks to make the statements true:
Show answer
(B) an isosceles right triangle 5
Q17Fill in the blanks
An angle greater than 180° and less than a complete angle is called _______.
Show answer
Reflex angle
Q18Fill in the blanks
The number of diagonals in a hexagon is ________.
Show answer
9
Q19Fill in the blanks
A pair of opposite sides of a trapezium are ________.
Show answer
Parallel
Q20Fill in the blanks
In Fig. 2.14, points lying in the interior of the triangle PQR are ______, that in the exterior are ______ and that on the triangle T N itself are ______. O Q M R Fig. 2.14 11.4.2018
This question refers to a figure in the original PDF.
Show answer
0 and S , T and N, M, P, Q, R
Q21Multiple choice
In Fig. 2.15, points A, B, C, D and E are collinear such that AB = BC = CD = DE. Then
This question refers to a figure in the original PDF.
- (a)AD = AB + ______
- (b)AD = AC + ______ Fig. 2.15
- (c)mid point of AE is ______
- (d)mid point of CE is ______ (e) AE = ______ × AB.
Show answer
(a) AD = AB + ______
(b) AD = AC + ______ Fig. 2.15
(c) mid point of AE is ______
(d) mid point of CE is ______ (e) AE = ______ × AB.
Q22Multiple choice
In Fig. 2.16,
This question refers to a figure in the original PDF.
- (a)∠AOD is a/an ______ angle
- (b)∠COA is a/an ______ angle
- (c)∠AOE is a/an ______ angle Fig. 2.16
Show answer
(a) ∠AOD is a/an ______ angle
(b) ∠COA is a/an ______ angle
(c) ∠AOE is a/an ______ angle Fig. 2.16
Q23Fill in the blanks
The number of triangles in Fig. 2.17 is ______. Their names are ______________________.
This question refers to a figure in the original PDF.
Show answer
5, ∆AOB, ∆AOC, ∆ACD, ∆COD, ∆ABC
Q24Fill in the blanks
Number of angles less than 180° in Fig. 2.17 is ______and their names are ______.
This question refers to a figure in the original PDF.
Show answer
12; ∠OAB, ∠OBA, ∠OAC, ∠OCA, ∠OCD, ∠ODC, ∠AOB, ∠AOC, ∠COD, ∠DOB, ∠BAC, ∠ACD
Q25Fill in the blanks
The number of straight angles in Fig. 2.17 is ______.
This question refers to a figure in the original PDF.
Show answer
Four
Q26Fill in the blanks
The number of right angles in a straight Fig. 2.17 angle is ______ and that in a complete angle is ______.
This question refers to a figure in the original PDF.
Show answer
Two, Four
Q27Fill in the blanks
The number of common points in the two angles marked in Fig. 2.18 is ______. E P Q C Fig. 2.18 11.4.2018
This question refers to a figure in the original PDF.
Show answer
Two,
Q28Fill in the blanks
The number of common points in the two angles marked in Fig. 2.19 is ______. B D A E Fig. 2.19
This question refers to a figure in the original PDF.
Show answer
One
Q29Fill in the blanks
The number of common points in the two angles marked in Fig. 2.20 ______ . E P D R C Fig. 2.20
This question refers to a figure in the original PDF.
Show answer
Three
Q30Fill in the blanks
The number of common points in the two angles marked in Fig. 2.21 is ______. A F G C Fig. 2.21 11.4.2018
This question refers to a figure in the original PDF.
Show answer
Four
Q31Fill in the blanks
The common part between the two angles BAC and DAB in Fig. 2.22 is ______. A C Fig. 2.22 State whether the statements given in questions 32 to 41 are true (T) or false (F):
This question refers to a figure in the original PDF.
Show answer
Ray AB
Q32Short answer
A horizontal line and a vertical line always intersect at right angles.
Show answer
T
Q33Short answer
If the arms of an angle on the paper are increased, the angle increases.
Show answer
F
Q34Short answer
If the arms of an angle on the paper are decreased, the angle decreases.
Show answer
F
Q35Short answer
If line PQ || line m, then line segment PQ || m
Show answer
T
Q36Short answer
Two parallel lines meet each other at some point.
Show answer
F
Q37Short answer
Measures of ∠ABC and ∠CBA in Fig. 2.23 are the same. B C Fig. 2.23
This question refers to a figure in the original PDF.
Show answer
T
Q38Short answer
Two line segments may intersect at two points.
Show answer
F
Q39Short answer
Many lines can pass through two given points.
Show answer
F
Q40Short answer
Only one line can pass through a given point.
Show answer
F
Q41Short answer
Two angles can have exactly five points in common.
Show answer
F
Q42Short answer
Name all the line segments in Fig. 2.24. Fig. 2.24 11.4.2018
This question refers to a figure in the original PDF.
Show answer
AB, AC, AD, AE, BC, BD, BE,CD, CE, DE
Q43Short answer
Name the line segments shown in Fig. 2.25. Fig. 2.25
This question refers to a figure in the original PDF.
Show answer
AB, BC, CD, DE, EA
Q44Short answer
State the mid points of all the sides of Fig. 2.26. A B Fig. 2.26
This question refers to a figure in the original PDF.
Show answer
X, Z, Y
Q45Short answer
Name the vertices and the line segments in Fig. 2.27. Fig. 2.27
This question refers to a figure in the original PDF.
Show answer
Vertices – A, B, C, D and E; line segments – AB, AC, AD, AE, BC, CD, DE
Q46Short answer
Write down fifteen angles (less than 180° ) involved in Fig. 2.28. E F B C Fig. 2.28 11.4.2018
This question refers to a figure in the original PDF.
Show answer
∠EAD, ∠AEF, ∠EFD, ∠ADF, ∠DFC, ∠DCF, ∠CDF, ∠BEF, ∠BFE, ∠EBF, ∠FBC, ∠FCB, ∠BFC, ∠ABC, ∠ACB ANSWERS 151 OOLRLPNOV _lqucpq
Q47Multiple choice
Name the following angles of Fig. 2.29, using three letters:
This question refers to a figure in the original PDF.
- (a)∠1 A
- (b)∠2
- (c)∠3 E
- (d)∠1 + ∠2 2 D (e) ∠2 + ∠3 B C (f) ∠1 + ∠2 + ∠3 (g) ∠CBA – ∠1 Fig. 2.29
Show answer
(a) ∠1 A
(b) ∠2
(c) ∠3 E
(d) ∠1 + ∠2 2 D (e) ∠2 + ∠3 B C (f) ∠1 + ∠2 + ∠3 (g) ∠CBA – ∠1 Fig. 2.29
Q48Multiple choice
Name the points and then the line segments in each of the following figures (Fig. 2.30):
This question refers to a figure in the original PDF.
- (i)
- (ii)
- (iii)
- (iv)Fig. 2.30
Show answer
(i)
(ii)
(iii)
(iv) Fig. 2.30
Q49Multiple choice
Which points in Fig. 2.31, appear to be mid-points of the line segments? When you locate a mid-point, name the two equal line segments formed by it. B D C
This question refers to a figure in the original PDF.
- (i)
- (ii)
- (iii)Fig. 2.31
Q50Multiple choice
Is it possible for the same
- (a)line segment to have two different lengths?
- (b)angle to have two different measures? 11.4.2018
Show answer
(a) line segment to have two different lengths?
(b) angle to have two different measures? 11.4.2018
Q51Short answer
Will the measure of ∠ABC and of ∠CBD make measure of ∠ABD in Fig. 2.32? B D Fig. 2.32
This question refers to a figure in the original PDF.
Show answer
Yes
Q52Short answer
Will the lengths of line segment AB and line segment BC make the length of line segment AC in Fig. 2.33? Fig. 2.33
This question refers to a figure in the original PDF.
Show answer
Yes
Q53Short answer
Draw two acute angles and one obtuse angle without using a protractor. Estimate the measures of the angles. Measure them with the help of a protractor and see how much accurate is your estimate.
Q54Multiple choice
Look at Fig. 2.34. Mark a point
This question refers to a figure in the original PDF.
- (a)A which is in the interior of both ∠1 and ∠2.
- (b)B which is in the interior of only ∠1.
- (c)Point C in the interior of ∠1. Now, state whether points B and C lie in the interior of ∠2 also. Fig. 2.34
Show answer
(b) B which is in the interior of only ∠1.
(c) Point C in the interior of ∠1. Now, state whether points B and C lie in the interior of ∠2 also. Fig. 2.34
Q55Multiple choice
Find out the incorrect statement, if any, in the following: An angle is formed when we have
- (a)two rays with a common end-point
- (b)two line segments with a common end-point
- (c)a ray and a line segment with a common end-point
Show answer
(b) two line segments with a common end-point
(c) a ray and a line segment with a common end-point
Q56Multiple choice
In which of the following figures (Fig. 2.35),
This question refers to a figure in the original PDF.
- (a)perpendicular bisector is shown? 11.4.2018
- (b)bisector is shown?
- (c)only bisector is shown?
- (d)only perpendicular is shown? (i) (ii) (iii) Fig. 2.35
Show answer
(a) perpendicular bisector is shown? 11.4.2018
(b) bisector is shown?
(c) only bisector is shown?
(d) only perpendicular is shown? (i) (ii) (iii) Fig. 2.35
Q57Multiple choice
What is common in the following figures
This question refers to a figure in the original PDF.
- (i)and
- (ii)(Fig. 2.36.)? (i) (ii) Fig. 2.36 Is Fig. 2.36 (i) that of triangle? if not, why?
Show answer
(i) and
Q58Short answer
If two rays intersect, will their point of intersection be the vertex of an angle of which the rays are the two sides?
Show answer
No
Q59Multiple choice
In Fig. 2.37, A D
This question refers to a figure in the original PDF.
- (a)name any four angles that appear to be acute angles. E
- (b)name any two angles that appear to be obtuse angles. B C Fig. 2.37
Show answer
(a) name any four angles that appear to be acute angles. E
(b) name any two angles that appear to be obtuse angles. B C Fig. 2.37
Q60Multiple choice
In Fig. 2.38,
This question refers to a figure in the original PDF.
- (a)is AC + CB = AB?
- (b)is AB + AC = CB?
- (c)is AB + BC = CA? A C B Fig. 2.38 11.4.2018
Show answer
(a) is AC + CB = AB?
(b) is AB + AC = CB?
(c) is AB + BC = CA? A C B Fig. 2.38 11.4.2018
Q61Multiple choice
In Fig. 2.39, A D
This question refers to a figure in the original PDF.
- (a)What is AE + EC?
- (b)What is AC – EC?
- (c)What is BD – BE? B C Fig. 2.39
- (d)What is BD – DE?
Show answer
(a) What is AE + EC?
(b) What is AC – EC?
(c) What is BD – BE? B C Fig. 2.39
(d) What is BD – DE?
Q62Multiple choice
Using the information given, name the right angles in each part of Fig. 2.40:
This question refers to a figure in the original PDF.
- (a)BA ⊥ BD
- (b)RT ⊥ ST
- (c)AC ⊥ BD
- (d)RS ⊥ RW (e) AC ⊥ BD (f) AE ⊥ CE (g) AC ⊥ CD (h) OP ⊥ AB Fig. 2.40 11.4.2018
Show answer
(a) BA ⊥ BD
(b) RT ⊥ ST
(c) AC ⊥ BD
(d) RS ⊥ RW (e) AC ⊥ BD (f) AE ⊥ CE (g) AC ⊥ CD (h) OP ⊥ AB Fig. 2.40 11.4.2018
Q63Multiple choice
What conclusion can be drawn from each part of Fig. 2.41, if
This question refers to a figure in the original PDF.
- (a)DB is the bisector of ∠ADC?
- (b)BD bisects ∠ABC?
- (c)DC is the bisector of ∠ ADB, CA ⊥ DA and CB ⊥ DB? Fig. 2.41
Show answer
(a) DB is the bisector of ∠ADC?
(b) BD bisects ∠ABC?
(c) DC is the bisector of ∠ ADB, CA ⊥ DA and CB ⊥ DB? Fig. 2.41
Q64Short answer
An angle is said to be trisected, if it is divided into three equal parts. If in Fig. 2.42, ∠ BAC = ∠ CAD = ∠ DAE, how many trisectors are there for ∠ BAE ? Fig. 2.42
This question refers to a figure in the original PDF.
Show answer
Two, AC and AD
Q65Short answer
How many points are marked in Fig. 2.43? Fig. 2.43
This question refers to a figure in the original PDF.
Show answer
Two
Q66Short answer
How many line segments are there in Fig. 2.43?
This question refers to a figure in the original PDF.
Show answer
One
Q67Short answer
In Fig. 2.44, how many points are marked? Name them.
This question refers to a figure in the original PDF.
Show answer
Three A, B, C
Q68Short answer
How many line segments are there in Fig. 2.44? Name them. Fig. 2.44 11.4.2018
This question refers to a figure in the original PDF.
Show answer
Three, AB, BC, AC
Q69Short answer
In Fig. 2.45 how many points are marked? Name them.
This question refers to a figure in the original PDF.
Show answer
Four, A, B, C, D
Q70Short answer
In Fig. 2.45 how many line segments are there? Name them. Fig. 2.45
This question refers to a figure in the original PDF.
Show answer
Six, AB, AC, AD, BC, BD, CD
Q71Short answer
In Fig. 2.46, how many points are marked? Name them.
This question refers to a figure in the original PDF.
Show answer
Five A, B, C, D, E
Q72Short answer
In Fig. 2.46 how many line segments are there? Name them. Fig. 2.46
This question refers to a figure in the original PDF.
Show answer
Ten, AB, AD, AE, AC, BD, BE, BC, DE, DC, EC
Q73Multiple choice
In Fig. 2.47, O is the centre of the circle.
This question refers to a figure in the original PDF.
- (a)Name all chords of the circle.
- (b)Name all radii of the circle.
- (c)Name a chord, which is not the diameter of the circle.
- (d)Shade sectors OAC and OPB. (e) Shade the smaller segment of the circle formed by CP. Fig. 2.47
Show answer
(a) Name all chords of the circle.
(b) Name all radii of the circle.
(c) Name a chord, which is not the diameter of the circle.
(d) Shade sectors OAC and OPB. (e) Shade the smaller segment of the circle formed by CP. Fig. 2.47
Q74Multiple choice
Can we have two acute angles whose sum is
- (a)an acute angle? Why or why not?
- (b)a right angle? Why or why not?
- (c)an obtuse angle? Why or why not?
- (d)a straight angle? Why or why not? (e) a reflex angle? Why or why not?
Show answer
(a) an acute angle? Why or why not?
(b) a right angle? Why or why not?
(c) an obtuse angle? Why or why not?
(d) a straight angle? Why or why not? (e) a reflex angle? Why or why not?
Q75Multiple choice
Can we have two obtuse angles whose sum is
- (a)a reflex angle? Why or why not?
- (b)a complete angle? Why or why not?
Show answer
(a) a reflex angle? Why or why not?
(b) a complete angle? Why or why not?
Q76Multiple choice
Write the name of
This question refers to a figure in the original PDF.
- (a)vertices
- (b)edges, and
- (c)faces of the prism shown in Fig. 2.48. Fig. 2.48 11.4.2018
Q77Short answer
How many edges, faces and vertices are there in a sphere?
Show answer
No edges, No faces and No vertices. E C
Q78Multiple choice
Draw all the diagonals of a pentagon ABCDE and name them. Activity 1: Observe questions 65 to 72. Can you find out the number of line segments, when the number of points marked on line segment is 7?, 9?, 10?. Activity 2: Copy the equilateral ∆ABC shown in Fig. 2.49 on your notebook.
This question refers to a figure in the original PDF.
- (a)Take a point P as shown in the figure.
- (b)Draw PD ⊥ BC , PE ⊥ CA and PF ⊥ AB
- (c)Also, draw AK ⊥ BC B KD C Fig. 2.49 Now, draw a line l, measure PD using a divider and ruler and mark it on line l as shown Fig. 2. 50. Fig. 2.50 Again measure PE with divider and mark it on the line l as DE (say). Again measure PF with divider and mark it on line l next to E as EF. 11.4.2018 Now check whether the length of AK and the length (PD + DE + EF) are the same! Activity 3: Copy the isosceles triangle ABC shown in Fig. 2.51 on your notebook. Take a point E on BC and draw EF ⊥ CA and EG ⊥ AB. Measure EF and EG and add them. Draw AD ⊥ BC . A Check whether the sum of EF and EG is equal to AD with the help of ruler or with the help of divider. B D E C Fig. 2.51 11.4.2018 MATHEMATICS Rough Work GEOMETRY 39 11.4.2018 UNIT-2 Rough Work 11.4.2018
Show answer
(a) Take a point P as shown in the figure.
(b) Draw PD ⊥ BC , PE ⊥ CA and PF ⊥ AB