NCERT Exemplar Class 6 Maths Geometry Solution: NCERT Exemplar Solution Class 6 Maths Chapter 2 Geometry Full Explanation. NCERT Exemplar Class 6 Maths – Chapter 2 Geometry. NCERT Exemplar Class 6 Maths Geometry Solution by Expert.
NCERT Exemplar Class 6 Maths Geometry Solution
Question 1:
Number of lines passing through five points such that no three of them are collinear is
(A) 10
(B) 5
(C) 20
(D) 8
Solution:
Correct answer is (A).
Number of lines passing through five pointed such that number three of them are collinear is 10.
Question 2:
The number of diagonals in a septagon is
(A) 21
(B) 42
(C) 7
(D) 14
Solution:
Correct answer is (D).
Number of diagonals in septagon is 14.
Question 3:
Number of line segments in Fig. 2.5 is
(A) 5
(B) 10
(C) 15
(D) 20
Solution:
Correct answer is (B).
Number of line segments in the fig. is 10.
Question 4:
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°
Solution:
Correct answer is (B).
Hours Hand is 270° & minute hand is 90°.
Question 5:
If a bicycle wheel has 48 spokes, then the angle between a pair of two consecutive spokes is
(A) (5 1/2)
(B) (7 1/2)
(C) (2/11)
(D) (2/15)
Solution:
Correct answer is (B).
Bicycle wheel has 48 spokes circle has 360° angle. So, we calculate the angle between a pair of two consecutive spoke is 360°/48 = 7 1/2
Question 6:
In Fig. 2.6, ∠XYZ cannot be written as
(A) ∠Y
(B) ∠ZXY
(C) ∠ZYX
(D) ∠XYP
Solution:
Correct answer is (B).
∠XY cannot be written as ∠ZXY because in ∠XYZ angle is Y an in option B angle is X.
Question 7:
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) greater than 45°
(B) 45°
(C) less than 45°
(D) 90°
Solution:
Correct answer is (B).
∠BPY = ∠APY = ∠XPY
Because all angle measurement is same all point lies in same ray i.e. ∠BPY = 45°.
Question 8:
The number of angles in Fig. 2.8 is
(A) 3
(B) 4
(C) 5
(D) 6
Solution:
Correct answer is (D).
The number of angles in above fig. is 6 each angle in this fig. assuming we give name to this angle.
∠BPY, ∠YPX, ∠XPZ, ∠BPX , ∠BPZ, ∠YPZ
Question 9:
The number of obtuse angles in Fig. 2.9 is
(A) 2
(B) 3
(C) 4
(D) 5
Solution:
Correct answer is (C).
Number of obtuse angle is 4 b y giving the name to their angle.
∠CFE, ∠BFD, ∠BFE, ∠AFD
Question 10:
The number of triangles in Fig. 2.10 is
(A) 10
(B) 12
(C) 13
(D) 14
Solution:
Correct answer is (B).
The number of angles in this fig is 12 assuming each triangle.
Question 11:
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.
Solution:
Correct answer is (D).
If the sum of two angle is greater than 180°, then two right angle is not possible.
Question 12:
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
Solution:
Correct answer is (D).
If the sum of two angles is equal to an obtuse angle, then two right angle is not possible.
Question 13:
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
Solution:
Correct answer is (B).
The number of diagonals of the polygon is 5. If a polygon has prime number of sides and Its number of sides is equal to the sum of the two least consecutive primes.
Question 14:
In Fig. 2.11, AB = BC and AD = BD = DC. The number of isosceles triangles in the figure is
(A) 1
(B) 2
(C) 3
(D) 4
Solution:
Correct answer is (B).
The number of isosceles triangles in the fig is 3 like as ∆ABD, ∆BDC, ∆ABC
Question 15:
In Fig. 2.12,
∠BAC = 90° and AD ⊥ BC.
The number of right triangles in the figure is
(A) 1
(B) 2
(C) 3
(D) 4
Solution:
Correct answer is (C).
The number of right triangles in the figure is 3. Fig. 2.12
∆ADC, ∆BDA, ∆ABC
Question 16:
In Fig. 2.13, PQ ⊥ RQ, PQ = 5 cm and QR = 5 cm. Then ∆PQR is
(A) a right triangle but not isosceles
(B) an isosceles right triangle
(C) isosceles but not a right triangle
(D) neither isosceles nor right triangle
Solution:
Correct answer is (B).
∆PQR is an isosceles right triangle because PQ = QR = 5 cm and PQ ⊥ RQ both condition match to condition of an isosceles right triangle.
In questions 17 to 31, fill in the blanks to make the statements true:
Question 17:
An angle greater than 180° and less than a complete angle is called ______.
Solution: An angle greater than 180° and less than a complete angle is called Reflex angle.
Question 18:
The number of diagonals in a hexagon is ______.
Solution: The number of diagonals in a hexagon is 9.
Question 19:
A pair of opposite sides of a trapezium are _____.
Solution: A pair of opposite sides of a trapezium are Parallel.
Question 20:
In Fig. 2.14, points lying in the interior of the triangle PQR are _____, that in the exterior are ______ and that on the triangle itself are _____.
Solution: Points lying in the interior of the triangle PQR are 0 and S, that in the exterior is T and N and that on the triangle itself are M, P, Q, R.
Question 21:
In Fig. 2.15, points A, B, C, D and E are collinear such that
AB = BC = CD = DE. Then
(a) AD = AB + _____
(b) AD = AC + _____
(c) mid point of AE is _____
(d) mid point of CE is _____
(e) AE = ____ × AB.
Solution:
(a) AD = AB + BD
(b) AD = AC + CD
(c) mid-point of AE is C
(d) mid-point of CE is D
(e) AE = 4 × AB.
Question 22:
In Fig. 2.16,
(a) ∠AOD is a/an _____ angle
(b) ∠COA is a/an _____ angle
(c) ∠AOE is a/an _____ angle
Solution:
(a) ∠AOD is a/an right angle
(b) ∠COA is a/an acute angle
(c) ∠AOE is a/an obtuse angle
Question 23:
The number of triangles in Fig. 2.17 is ______.
Their names are _______.
Solution:
The number of triangles in Fig. 2.17 is 5.
Their names are ∆AOB, ∆AOC, ∆ACD, ∆COD, ∆ABC.
Question 24:
Number of angles less than 180° in Fig. 2.17 is ______and their names are ______.
Solution:
Number of angles less than 180° in Fig. 2.17 is 12 and their names are ∠OAB, ∠OBA, ∠OAC, ∠OCA, ∠OCD, ∠ODC, ∠AOB, ∠AOC, ∠COD, ∠DOB, ∠BAC, ∠ACD.
Question 25:
The number of straight angles in Fig. 2.17 is ______.
Solution:
The number of straight angles in Fig. 2.17 is four.
Question 26:
The number of right angles in a straight angle is _____ and that in a complete angle is _____.
Solution: The number of right angles in a straight angle is Two and that in a complete angle is Four.
Question 27:
The number of common points in the two angles marked in Fig. 2.18 is ______.
Solution:
The number of common points in the two angles marked in Fig. 2.18 is Two.
Question 28:
The number of common points in the two angles marked in Fig. 2.19 is ______.
Solution:
The number of common points in the two angles marked in Fig. 2.19 is one.
Question 29:
The number of common points in the two angles marked in Fig. 2.20 ______ .
Solution:
The number of common points in the two angles marked in Fig. 2.20 Three.
Question 30:
The number of common points in the two angles marked in Fig. 2.21 is ______.
Solution:
The number of common points in the two angles marked in Fig. 2.21 is four.
Question 31:
The common part between the two angles BAC and DAB in Fig. 2.22 is ______.
Solution:
The common part between the two angles BAC and DAB in Fig. 2.22 is Ray AB.
State whether the statements given in questions 32 to 41 are true (T) or false (F):
Question 32:
A horizontal line and a vertical line always intersect at right angles.
Solution: Statement is True.
Question 33:
If the arms of an angle on the paper are increased, the angle increases.
Solution: Statement is false. Number is not true because if the arms of an angle on the paper is increased, the angle remains as it is.
Question 34:
If the arms of an angle on the paper are decreased, the angle decreases.
Solution: Statement is false. If the arms of an angle on the paper are decreased, the angle remains as it is.
Question 35:
If line PQ || line m, then line segment PQ || m
Solution: Statement is True.
Question 36:
Two parallel lines meet each other at some point.
Solution: Statement is false. Because two parallel lines never meet each other at some point.
Question 37:
Measures of ∠ABC and ∠CBA in Fig. 2.23 are the same.
Solution: Statement is True.
Question 38:
Two line segments may intersect at two points.
Solution: Statement is false. Two-line segments don’t intersect at two points.
Question 39:
Many lines can pass through two given points.
Solution: Statement is false. Many lines can’t pass through given points.
Question 40:
Only one line can pass through a given point.
Solution: Statement is false. Many lines can pass through given points.
Question 41:
Two angles can have exactly five points in common.
Solution: Statement is false. Two angles can’t have exactly five points in common.
Question 42:
Name all the line segments in Fig. 2.24.
Solution: All the line segment in this fig are line AB, line AC, line AD, line AE, line BC, line BD, line BF, line CD, line CE.
Question 43:
Name the line segments shown in Fig. 2.25.
Solution: AB, BC, CD, DE, EF This are in the line segment in fig.
Question 44:
State the mid points of all the sides of Fig. 2.26.
Solution: X, Y, Z there are the midpoint of all the sides.
Question 45:
Name the vertices and the line segments in Fig. 2.27.
Solution: Line segment = AB, AC, AD, AE,BC, CD, DF
Vertices = A, B, C, D, E These all the vertices and line segment in this fig.
Question 46:
Write down fifteen angles (less than 180°) involved in Fig. 2.28.
Solution:
∠AEF, ∠EAD, ∠ADF, ∠EFD, ∠DFC, ∠DCF, ∠BEF, ∠CDF, ∠BFE, ∠EBF, ∠FBC, Fig. 2.28. ∠FCB, ∠BFC, ∠ABC, ∠ACB These are the fifteen angles less than 180° in this fig.
Question 47:
Name the following angles of Fig. 2.29, using three letters:
(a) ∠1
(b) ∠2
(c) ∠3
(d) ∠1 + ∠2
(e) ∠2 + ∠3
(f) ∠1 + ∠2 + ∠3
(g) ∠CBA – ∠1
Solution:
Following are the angle using three letters.
(a) ∠1 = ∠CBD
(b) ∠2 = ∠DBE
(c) ∠3 = ∠EBA
(d) ∠1 + ∠2 = ∠CBE
(e) ∠2 + ∠3 = ∠DBA
(f) ∠1 + ∠2 + ∠3 = ∠CBA
(g) ∠CBA – ∠1 = ∠DBA
Question 48:
Name the points and then the line segments in each of the following figures (Fig. 2.30):
Solution:
(i) Point A, Point B, Point C and the line AB, line AC, line BC.
(ii) Point A, B, C, D and the line segment AB, BC, CD, AD.
(iii) Point A, B, C, D and the line segment AB, BC, CD, DE.
(iv) Point A, B, C, D, E, F and the line segment AB, CD, EF.
Question 49:
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.
Solution:
(iii) D is the midpoint of the line segment and DC, DB are two equal line segment.
(ii) o is the midpoint of the line segment and OA and OB are two equal line segment.
Question 50:
Is it possible for the same
(a) line segment to have two different lengths?
(b) angle to have two different measures?
Solution:
(a) No, it is not possible line segment to have two different lengths.
(b) No, it Is not possible angle to have two different measures.
Question 51:
Will the measure of ∠ABC and of ∠CBD make measure of ∠ABD in Fig. 2.32?
Solution: Because ∠ABC + ∠CBD = ∠ABD Hence the measure of ∠ABC and of ∠CBD make measure of ∠ABD.
Question 52:
Will the lengths of line segment AB and line segment BC make the length of line segment AC in Fig. 2.33?
Solution: Yes, because AB + BC = AC, Hence the length of line segment AB and line segment BC make the length of line segment AC.
Question 53:
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.
Solution:
Question 54:
Look at Fig. 2.34. Mark a point
(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.
Solution: Yes, Point B and C lie in the interior ofÐ2 also by seeing following fig.
Question 55:
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
Solution:
b and c are the incorrect statement.
(b) = two-line segments with a common end-point.
(c) = a ray and a line segment with a common end-point.
Question 56:
In which of the following figures (Fig. 2.35),
(a) perpendicular bisector is shown?
(b) bisector is shown?
(c) only bisector is shown?
(d) only perpendicular is shown?
Solution:
(a) Following fig show the perpendicular bisector.
(b) Following fig show the bisector.
(c) Following fig show the only bisector.
(d) Following fig show the only perpendicular.
Question 57:
What is common in the following figures (i) and (ii) (Fig. 2.36.)?
Is Fig. 2.36 (i) that of triangle? if not, why?
Solution:
Both fig have 3 line segment but (i) is just a fig and (ii) is triangle. Hence it is not a closed figure or triangle.
Question 58:
If two rays intersect, will their point of intersection be the vertex of an angle of which the rays are the two sides?
Solution: No, if two rays intersect, will their point of intersection not the vertex of an angle of which the rays are the two sides.
Question 59:
In Fig. 2.37,
(a) name any four angles that appear to be acute angles.
(b) name any two angles that appear to be obtuse angles.
Solution:
(a) = ∠ABE, ∠BCE, ∠BAE, ∠AEB are the four acute angle of this fig
(b) = ∠BAD, ∠BCD are the obtuse angle made by this figure.
Question 60:
In Fig. 2.38,
(a) is AC + CB = AB?
(b) is AB + AC = CB?
(c) is AB + BC = CA?
Solution:
(a) Yes , AC + CB = AB is true
(b) No, AB + AC = CB is not true
(c) No, AB + AC = CB is not true
Question 61:
In Fig. 2.39,
(a) What is AE + EC?
(b) What is AC – EC?
(c) What is BD – BE?
(d) What is BD – DE?
Solution:
(a) AE + EC = AC
(b) AC – EC = AE
(c) BD – BE = ED
(d) BD – DE = BE3
Question 62:
Using the information given, name the right angles in each part of Fig. 2.40:
Solution:
(a) BA ⊥ BD made an angle ∠ABD
(b) RT ⊥ ST made an angle ∠RTS.
(c) AC ⊥ BD made an angle ∠ACB and ∠ACD.
(d) RT ⊥ ST made an angle ∠RTS and ∠RTW
(e) AC ⊥ BD made an angle ∠AEB, ∠AFD, ∠BEC and ∠DEC
(f) AE ⊥ CE made an angle ∠AEC.
(g) AC ⊥ CD made an angle ∠ACD.
(h) OP ⊥ AB made an angle ∠AKP, ∠BKO,∠AKO and ∠BKP.
Question 63:
What conclusion can be drawn from each part of Fig. 2.41, if
(a) DB is the bisector of ∠ADC?
(b) BD bisects ∠ABC?
(c) DC is the bisector of ∠ADB, CA ⊥ DA and CB ⊥ DB?
Solution:
(a) We drawn a conclusion that is ∠ADB = ∠COD.
(b) We drawn a conclusion that is ∠ABD = ∠CBD.
(c) We drawn a conclusion that is ∠ADC= ∠BDC and ∠CAD = 90°, ∠CBD = 90°.
Question 64:
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?
Solution: Two Trisector are these for ∠BAE in this figure and that is AD and AC.
Question 65:
How many points are marked in Fig. 2.43?
Solution: Two.
Question 66:
How many line segments are there in Fig. 2.43?
Solution: One.
Question 67:
In Fig. 2.44, how many points are marked? Name them.
Solution: Three A, B and C.
Question 68:
How many line segments are there in Fig. 2.44? Name them.
Solution: Three AB, BC, AC.
Question 69:
In Fig. 2.45 how many points are marked? Name them.
Solution: Four A, B, C, D.
Question 70:
In Fig. 2.45 how many line segments are there? Name them.
Solution: Six AB, AC, AD, BC, BD, CD.
Question 71:
In Fig. 2.46, how many points are marked? Name them.
Solution: Five A, B, C, D, E.
Question 72:
In Fig. 2.46 how many line segments are there? Name them
Solution: Ten AB, AC, AD, AE.BD, BE, BC, DE, DC, EC.
Question 73:
In Fig. 2.47, O is the centre of the circle.
(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.
Solution:
(a) CP and AB are the chords of the circle.
(b) OB, OA, OP , OC are radii of the circle.
(c) CP is the chord which I not the diameter of the circle.
(d)
(e)
Question 74:
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?
Solution:
(a) Yes because the sum of two acute angle may be less than a right angle, means It may be an acute angle.
(b) Yes, the sum of two acute angle may be equal to a right angle.
(c) Yes, Because the sum of two acute angle may be more than right angle or maybe obtuse angle.
(d) No, because sum of two acute angle is always less than 180°.
(e) No, because the sum of two angle is always less than 180 °.
Question 75:
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?
Solution:
(a) Yes, Because the sum of two obtuse angle is always greater than 180°
(b) No, Because the sum of two is always greater than 180° but than 360°.
Question 76:
Write the name of
(a) vertices
(b) edges, and
(c) faces of the prism shown in Fig. 2.48.
Solution:
(a) A, B, C, D, E, F are vertices of three figure.
(b) AB, AC, BD, BC, FC, DF, EF, AF, ED are the edges of this fig.
(c) ABC, DEF, AEDB, BDFC, AEFC are the faced of this given fig.
Sphere does not have any edges vertices and faces.
Question 77:
How many edges, faces and vertices are there in a sphere?
Solution: Sphere does not have any edge vertices and face.
Question 78:
Draw all the diagonals of a pentagon ABCDE and name them.
Solution: AD, BE CE, BD, AC are the diagonals of the pentagon.
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