CBSE Class 9 Mental Maths Introduction To Euclids Geometry Worksheet

Question. Which are the two greek words, the word ‘geomentry’ has been derived from?
Answer : ‘geo’ and ‘metrien’

Question. What is the meaning of these two words?
Answer : ‘Geo’ means ‘the earth’ ‘metrien’ meand ‘measure

Question. What does the word ‘geometry’ mean?
Answer : ‘measurement of the earth’

Question. Who were the first people to study geometry?
Answer : The enciant Egypticians and the babylonians.

Question. Who were the people who used the knowledge of geomentry for calculating areas of fields and volume of grain storehouses.
Answer : The Egypticians

Question. Who developed formulae for areas of rectilinear figures such as rectangles and traiangles.
Answer : The Babylonians

Question. To whom goes the credit for the systematic study of geometry.
Answer : The Greeks

Question. Name the two most well known greek Mathematicians?
Answer : Thales and Pythagoras

Question. Who is known as the ‘father of geometry’?
Answer : Euclid

Question. What is the name of Euclid’s most famous work?
Answer : Elements

Question. Name two Indian mathematicians who contributed significantly in the field of geometry?
Answer : Brahamgupt, Bhaskar II, Aryabhatt

Question. What is the difference between axioms and postulates?
Answer : Axioms are the common nations (as sumptions) used throughout mathematics and not specially linket to gerometry.
Postupates are the assumptions specific to geometry.

Question. State Euclid’s postulate for a straight line.
Answer : A strainght line may be drawn from any Egypticians one point to any other point

Question. State Euclid’s postulate for a straight circle.
Answer : A circle can be drawn with any radius and any centre

Question. What is Euclid’s postulate on right angles?
Answer : All right angles are equal to one another

Question. What is Euclid’s fifth postulate ?
Answer : If a staright line falling on two straight lines make the interior angles on the same side
of it taken together less then two right angles, if produced indefinitely, meet on that side
on which the sum of angles is less than two right angles.

Question. Who restated the fifth postulate of Euclid’s?
Answer : John Playfair in 1729

Question. What is the name given to restated form of Euclid’s fifth postulate?
Answer : Playfair’s Axiom

Question. Give the statement of restated form of Euclid’s fifth postulate?
Answer : Two distinct intersecting lines cannot be parallel to the same line.

Question. What is the difference between axioms and Theorems?
Answer : Axioms are the basic facts which are taken for granted without proof. They are obvious
universal truth.
Theorems are statement which are proved through logical reasoning based on previously
proved results and some Axioms

Question. What is the historical importance of Euclid’s fifth postulate?
Answer : Inspite of several attempts till today, this postulate could not be proved as a theo
rem . Moreover, these attempts have led to the creation of different other geometries known as non-euclidean geometries

Question. What is the least number of distinct points which determine a unique line?
Answer : Two

Question. In how many maximum numbers of points can two distinct lines intersect?
Answer : One

Question. State playfair’s Axiom.
Answer : Two distinct intersecting lines cannot be parallel to the same line.

Question. What is the name of the work that contained Euclid’s thirteen volumes?
Answer : Elements

Question. How many lines can be drawn through a single point?
Answer : Elements

Question. Can two distinct intersecting lines be parallel to the same line? Why?
Answer : No, Playfair’s Axiom

Question. Given two points L and M, how many line segments do they determine?
Answer : One

Question. Name the line segments determined by three collinear points x, y and z?
Answer : XY, YZ, ZX

Question. What are the three basic concepts in geometry?
Answer : Point, line and plane

Fill in the blanks: 

Question. Things which are equal to the same things are ____________ to one another.
Answer : Equal

Question. The ____________ is greater than the part.
Answer : Whole

Question. Things which are double of the ______________ are equal to one another.
Answer : Same thing

Question. Two distinct point in a plane determine a _____________ line.
Answer : Unique

Question. A line seperates a plane into _____________ parts namely the ____________ and the _____________ itself.
Answer : Three, two half planes, line

Question. Two distinct _____________ in a plane cannot have more than one point in common.
Answer : lines

Question. Given line and a point, not on the line, there is one and only one ______________ line which passes through the given point and is _____________ to the line.
Answer : perpendicular, perpendicular

Question. If B lies between A and C, AC = 15 cm, BC = 9 cm, what is (AB)2
Answer : 36

Question. Does a line have any length.
Answer : Yes (Breadthless

Question. Give an example of geometrical straight line.
Answer : The edge of the ruler

Question. In fig 1 name the following
(i) 3 line segments
(ii) 4 collinear points
(iii) a pair of non-intersecting line segments.
Answer : (i) AC, BQ, RS (ii) C,D, Q, S (iii) AC, BQ

Question. What is the difference between intersecting lines and concurrent lines?
Answer : When two lines have a common point they are called intersecting lines.
When more then two lines have a common point, they are called concurrent lines.

Question. State parallel Axiom.
Answer : If l is a line and P is point not on line l, there is one and only one line which passes,
thnrough p and is parallel to l.

Question. If line AB, AC, AD, AR are parallel to a line l, then points A, B, C, D and R are _______________.
Answer : Collinear

Question. What do you understand ‘betweenness’?
Answer : A point C is said to lie between two points A & B if A, B and C are collinear points and
AC + CB = AB

46. Explain mid point of a line segment with the help of an example.
Answer : A point M is said to be the mid point of AB if M is an interior point of AB and AM = MB

Question. Explain congruence of line segments.
Answer : If two line segments have equal lengths, they are congruent to one another.

Question. Give the definition of the point as given by Euclid.
Answer : A point is that which has no part

Question. Give the definition of a ‘line’ as given by Euclid.
Answer : A line is breadthless length.

Question. With reference to the fig 2 given below, state which statement is true and which is false.
(i) PQ + QR = PR
(ii) PR + PS = PS
(iii) Lines PQ and PS are coincident.
(iv) Points R, S, T lie on the line PQ.
Answer : (i) True (ii) False (iii) True (iv) True