# NCERT solutions for Mathematics Exemplar Class 6 chapter 2 - Geometry [Latest edition]

## Chapter 2: Geometry

Exercise
Exercise [Pages 23 - 37]

### NCERT solutions for Mathematics Exemplar Class 6 Chapter 2 Geometry Exercise [Pages 23 - 37]

#### Choose the correct alternative:

Exercise | Q 1 | Page 23

Number of lines passing through five points such that no three of them are collinear is ______.

• 10

• 5

• 20

• 8

Exercise | Q 2 | Page 24

The number of diagonals in a septagon is ______.

• 21

• 42

• 7

• 14

Exercise | Q 3 | Page 24

Number of line segments in Figure is ______.

• 5

• 10

• 15

• 20

Exercise | Q 4 | Page 24

Measures of the two angles between hour and minute hands of a clock at 9 O’ clock are ______.

• 60°, 300°

• 270°, 90°

• 75°, 285°

• 30°, 330°

Exercise | Q 5 | Page 24

If a bicycle wheel has 48 spokes, then the angle between a pair of two consecutive spokes is ______.

• (5 1/2)

• (7 1/2)

• (2/11)

• (2/15)

Exercise | Q 6 | Page 24

In figure, ∠XYZ cannot be written as ______.

• ∠Y

• ∠ZXY

• ∠ZYX

• ∠XYP

Exercise | Q 7 | Page 24

In figure, if point A is shifted to point B along the ray PX such that PB = 2PA, then the measure of ∠BPY is ______.

• Greater than 45°

• 45°

• Less than 45°

• 90°

Exercise | Q 8 | Page 24

The number of angles in figure is ______.

• 3

• 4

• 5

• 6

Exercise | Q 9 | Page 25

The number of obtuse angles in figure is ______.

• 2

• 3

• 4

• 5

Exercise | Q 10 | Page 25

The number of triangles in figure is ______.

• 10

• 12

• 13

• 14

Exercise | Q 11 | Page 25

If the sum of two angles is greater than 180°, then which of the following is not possible for the two angles?

• One obtuse angle and one acute angle

• One reflex angle and one acute angle

• Two obtuse angles

• Two right angles

Exercise | Q 12 | Page 25

If the sum of two angles is equal to an obtuse angle, then which of the following is not possible?

• One obtuse angle and one acute angle.

• One right angle and one acute angle

• Two acute angles

• Two right angles

Exercise | Q 13 | Page 25

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 ______.

• 4

• 5

• 7

• 10

Exercise | Q 14 | Page 26

In figure, AB = BC and AD = BD = DC. The number of isosceles triangles in the figure is ______.

• 1

• 2

• 3

• 4

Exercise | Q 15 | Page 26

In figure, ∠BAC = 90° and AD ⊥ BC. The number of right triangles in the figure is ______.

• 1

• 2

• 3

• 4

Exercise | Q 16 | Page 26

In figure, PQ ⊥ RQ, PQ = 5 cm and QR = 5 cm. Then ∆PQR is ______.

• A right triangle but not isosceles

• An isosceles right triangle

• Isosceles but not a right triangle

• Neither isosceles nor right triangle

#### Fill in the blank:

Exercise | Q 17 | Page 26

An angle greater than 180° and less than a complete angle is called ______.

Exercise | Q 18 | Page 26

The number of diagonals in a hexagon is ______.

Exercise | Q 19 | Page 26

A pair of opposite sides of a trapezium are ______.

Exercise | Q 20 | Page 26

In figure, points lying in the interior of the triangle PQR are ______, that in the exterior are ______ and that on the triangle itself are ______.

Exercise | Q 21.(a) | Page 27

In figure, points A, B, C, D and E are collinear such that AB = BC = CD = DE. Then

Exercise | Q 21.(b) | Page 27

In figure, points A, B, C, D and E are collinear such that AB = BC = CD = DE. Then

Exercise | Q 21.(c) | Page 27

In figure, points A, B, C, D and E are collinear such that AB = BC = CD = DE. Then

Mid point of AE is ______

Exercise | Q 21.(d) | Page 27

In figure, points A, B, C, D and E are collinear such that AB = BC = CD = DE. Then

Midpoint of CE is ______

Exercise | Q 21.(e) | Page 27

In figure, points A, B, C, D and E are collinear such that AB = BC = CD = DE. Then

AE = ______ × AB.

Exercise | Q 22.(a) | Page 27

In the given figure.

∠AOD is a/an ____ angle

Exercise | Q 22.(b) | Page 27

In the given figure.

∠COA is a/an ______ angle

Exercise | Q 22.(c) | Page 27

In the given figure.

∠AOE is a/an ______ angle

Exercise | Q 23 | Page 27

The number of triangles in figure is ______. Their names are ______.

Exercise | Q 24 | Page 27

Number of angles less than 180° in figure is ______ and their names are ______.

Exercise | Q 25 | Page 27

The number of straight angles in figure is ______.

Exercise | Q 26 | Page 27

The number of right angles in a straight angle is ______ and that in a complete angle is ______.

Exercise | Q 27 | Page 27

The number of common points in the two angles marked in figure is ______.

Exercise | Q 28 | Page 28

The number of common points in the two angles marked in figure is ______.

Exercise | Q 29 | Page 28

The number of common points in the two angles marked in figure ______.

Exercise | Q 30 | Page 28

The number of common points in the two angles marked in figure is ______.

Exercise | Q 31 | Page 29

The common part between the two angles BAC and DAB in figure is ______.

#### State whether the following statement is True or False:

Exercise | Q 32 | Page 29

A horizontal line and a vertical line always intersect at right angles.

• True

• False

Exercise | Q 33 | Page 29

If the arms of an angle on the paper are increased, the angle increases.

• True

• False

Exercise | Q 34 | Page 29

If the arms of an angle on the paper are decreased, the angle decreases.

• True

• False

Exercise | Q 35 | Page 29

If line PQ || line m, then line segment PQ || m.

• True

• False

Exercise | Q 36 | Page 29

Two parallel lines meet each other at some point.

• True

• False

Exercise | Q 37 | Page 29

Measures of ∠ABC and ∠CBA in figure are the same.

• True

• False

Exercise | Q 38 | Page 29

Two line segments may intersect at two points.

• True

• False

Exercise | Q 39 | Page 29

Many lines can pass through two given points.

• True

• False

Exercise | Q 40 | Page 29

Only one line can pass through a given point.

• True

• False

Exercise | Q 41 | Page 29

Two angles can have exactly five points in common.

• True

• False

Exercise | Q 42 | Page 29

Name all the line segments in figure

Exercise | Q 43 | Page 30

Name the line segments shown in figure.

Exercise | Q 44 | Page 30

State the midpoints of all the sides of figure.

Exercise | Q 45 | Page 30

Name the vertices and the line segments in figure.

Exercise | Q 46 | Page 30

Write down fifteen angles (less than 180°) involved in figure.

Exercise | Q 47.(a) | Page 31

Name the following angles of figure, using three-letter:

∠1

Exercise | Q 47.(b) | Page 31

Name the following angles of figure, using three-letter:

∠2

Exercise | Q 47.(c) | Page 31

Name the following angles of figure, using three-letter:

∠3

Exercise | Q 47.(d) | Page 31

Name the following angles of figure, using three-letter:

∠1 + ∠2

Exercise | Q 47.(e) | Page 31

Name the following angles of figure, using three-letter:

∠2 + ∠3

Exercise | Q 47.(f) | Page 31

Name the following angles of figure, using three-letter:

∠1 + ∠2 + ∠3

Exercise | Q 47.(g) | Page 31

Name the following angles of figure, using three-letter:

∠CBA – ∠1

Exercise | Q 48.(i) | Page 31

Name the points and then the line segments in the following figure:

Exercise | Q 48.(ii) | Page 31

Name the points and then the line segments in the following figure:

Exercise | Q 48.(iii) | Page 31

Name the points and then the line segments in the following figure:

Exercise | Q 48.(iv) | Page 31

Name the points and then the line segments in the following figure:

Exercise | Q 49.(i) | Page 31

Which points in figure, appear to be mid-points of the line segments? When you locate a mid-point, name the two equal line segments formed by it.

Exercise | Q 49.(ii) | Page 31

Which points in figure, appear to be mid-points of the line segments? When you locate a mid-point, name the two equal line segments formed by it.

Exercise | Q 49.(iii) | Page 31

Which points in figure, appear to be mid-points of the line segments? When you locate a mid-point, name the two equal line segments formed by it.

Exercise | Q 50.(a) | Page 31

Is it possible for the same line segment to have two different lengths?

Exercise | Q 50.(b) | Page 31

Is it possible for the same angle to have two different measures?

Exercise | Q 51 | Page 32

Will the measure of ∠ABC and of ∠CBD make measure of ∠ABD in figure?

Exercise | Q 52 | Page 32

Will the lengths of line segment AB and line segment BC make the length of line segment AC in figure?

Exercise | Q 53 | Page 32

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

Exercise | Q 54 | Page 32

Look at a given figure. 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.

Exercise | Q 55 | Page 32

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

Exercise | Q 56.(a) | Page 32

In which of the following figures, perpendicular bisector is shown?

Exercise | Q 56.(b) | Page 32

In which of the following figures, bisector is shown?

Exercise | Q 56.(c) | Page 32

In which of the following figures, only bisector is shown?

Exercise | Q 56.(d) | Page 32

In which of the following figures, only perpendicular is shown?

Exercise | Q 57 | Page 33

What is common in the following figure?

 (i) (ii)

Is figure (i) that of triangle? if not, why?

Exercise | Q 58 | Page 33

If two rays intersect, will their point of intersection be the vertex of an angle of which the rays are the two sides?

Exercise | Q 59.(a) | Page 33

In given figure, name any four angles that appear to be acute angles.

Exercise | Q 59.(b) | Page 33

In given figure, name any two angles that appear to be obtuse angles.

Exercise | Q 60.(a) | Page 33

In given figure, is AC + CB = AB ?

Exercise | Q 60.(b) | Page 33

In given figure, is AB + AC = CB?

Exercise | Q 60.(c) | Page 33

In given figure, is AB + BC = CA?

Exercise | Q 61.(a) | Page 34

In given figure, What is AE + EC?

Exercise | Q 61.(b) | Page 34

In given figure, What is AC – EC?

Exercise | Q 61.(c) | Page 34

In given figure, What is BD – BE?

Exercise | Q 61.(d) | Page 34

In given figure, What is BD – DE?

Exercise | Q 62.(a) | Page 34

Using the information given, name the right angles in part of figure:

BA ⊥BD

Exercise | Q 62.(b) | Page 34

Using the information given, name the right angles in part of figure:

RT ⊥ ST

Exercise | Q 62.(c) | Page 34

Using the information given, name the right angles in part of figure:

AC ⊥ BD

Exercise | Q 62.(d) | Page 34

Using the information given, name the right angles in part of figure:

RS ⊥ RW

Exercise | Q 62.(e) | Page 34

Using the information given, name the right angles in part of figure:

AC ⊥ BD

Exercise | Q 62.(f) | Page 34

Using the information given, name the right angles in part of figure:

AE ⊥ CE

Exercise | Q 62.(g) | Page 34

Using the information given, name the right angles in part of figure:

AC ⊥ CD

Exercise | Q 62.(h) | Page 34

Using the information given, name the right angles in part of figure:

OP ⊥ AB

Exercise | Q 63.(a) | Page 35

What conclusion can be drawn from part of given figure, if DB is the bisector of ∠ADC?

Exercise | Q 63.(b) | Page 35

What conclusion can be drawn from part of given figure, if BD bisects ∠ABC?

Exercise | Q 63.(c) | Page 35

What conclusion can be drawn from part of given figure, if DC is the bisector of ∠ADB, CA ⊥ DA and CB ⊥ DB?

Exercise | Q 64 | Page 35

An angle is said to be trisected, if it is divided into three equal parts. If in the given figure, ∠BAC = ∠CAD = ∠DAE, how many trisectors are there for ∠BAE?

Exercise | Q 65 | Page 35

How many points are marked in the figure?

Exercise | Q 66 | Page 35

How many line segments are there in given figure?

Exercise | Q 67 | Page 35

In the given, how many points are marked? Name them.

Exercise | Q 68 | Page 35

How many line segments are there in given figure? Name them.

Exercise | Q 69 | Page 36

In the given figure, how many points are marked? Name them.

Exercise | Q 70 | Page 36

In given figure how many line segments are there? Name them.

Exercise | Q 71 | Page 36

In given figure, how many points are marked? Name them.

Exercise | Q 72 | Page 36

In given figure how many line segments are there? Name them.

Exercise | Q 73.(a) | Page 36

In the given figure, O is the centre of the circle. Name all chords of the circle.

Exercise | Q 73.(b) | Page 36

In the given figure, O is the centre of the circle. Name all radii of the circle.

Exercise | Q 73.(c) | Page 36

In the given figure, O is the centre of the circle. Name a chord, which is not the diameter of the circle.

Exercise | Q 73.(d) | Page 36

In the given figure, O is the centre of the circle. Shade sectors OAC and OPB.

Exercise | Q 73.(e) | Page 36

In the given figure, O is the centre of the circle. Shade the smaller segment of the circle formed by CP.

Exercise | Q 74.(a) | Page 36

Can we have two acute angles whose sum is an acute angle? Why or why not?

Exercise | Q 74.(b) | Page 36

Can we have two acute angles whose sum is a right angle? Why or why not?

Exercise | Q 74.(c) | Page 36

Can we have two acute angles whose sum is an obtuse angle? Why or why not?

Exercise | Q 74.(d) | Page 36

Can we have two acute angles whose sum is a straight angle? Why or why not?

Exercise | Q 74.(e) | Page 36

Can we have two acute angles whose sum is a reflex angle? Why or why not?

Exercise | Q 75.(a) | Page 36

Can we have two obtuse angles whose sum is an acute angle? Why or why not?

Exercise | Q 75.(b) | Page 36

Can we have two obtuse angles whose sum is a complete angle? Why or why not?

Exercise | Q 76.(a) | Page 36

Write the name of vertices

Exercise | Q 76.(b) | Page 36

Write the name of edges

Exercise | Q 76.(c) | Page 36

Write the name of faces of the prism shown in given figure.

Exercise | Q 77 | Page 37

How many edges, faces and vertices are there in a sphere?

Exercise | Q 78 | Page 37

Draw all the diagonals of a pentagon ABCDE and name them.

Exercise

## NCERT solutions for Mathematics Exemplar Class 6 chapter 2 - Geometry

NCERT solutions for Mathematics Exemplar Class 6 chapter 2 (Geometry) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics Exemplar Class 6 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Mathematics Exemplar Class 6 chapter 2 Geometry are Concept for Basic Geometrical Ideas (2 -d), Concept of Points, Concept of Line, Concept of Line Segment, Concept of Ray, Concept of Intersecting Lines, Parallel Lines, Concept of Curves, Different Types of Curves - Closed Curve, Open Curve, Simple Curve., Concept of Polygons - Side, Vertex, Adjacent Sides, Adjacent Vertices and Diagonal, Concept of Angle - Arms, Vertex, Interior and Exterior Region, Concept of Triangles - Sides, Angles, Vertices, Interior and Exterior of Triangle, Concept of Quadrilaterals - Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles, Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles.

Using NCERT Class 6 solutions Geometry exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 6 prefer NCERT Textbook Solutions to score more in exam.

Get the free view of chapter 2 Geometry Class 6 extra questions for Mathematics Exemplar Class 6 and can use Shaalaa.com to keep it handy for your exam preparation