Class 4 Maths - Geometry - CBSE Worksheets

Multiple Choice Questions

Q1: Which Greek mathematician is often referred to as the "Father of Geometry"?
(a) Pythagoras
(b) Euclid
(c) Archimedes
(d) Thales
Ans: (b)
Euclid is considered the "Father of Geometry" because of his significant contributions to the field. He compiled the principles, postulates, and theorems of geometry in his book "Elements," which became a fundamental work in the subject.

Q2: Which branch of mathematics primarily deals with the shapes and sizes of objects?
(a) Algebra
(b) Calculus
(c) Geometry
(d) Trigonometry
Ans: (c)
Geometry is the branch of mathematics that focuses on the properties and relationships of shapes, sizes, angles, and spatial dimensions. It studies the fundamental concepts of points, lines, curves, and solids.

Q3: Which type of geometry is based on Euclid's axioms and postulates?
(a) Euclidean Geometry
(b) Hyperbolic Geometry
(c) Elliptical Geometry
(d) Spherical Geometry
Ans: (a)
Euclidean Geometry is the type of geometry based on Euclid's axioms and postulates. It is the study of plane and solid figures on the basis of assumptions and logical reasoning.

Q4: What is the sum of the angles in a triangle in spherical geometry?
(a) 90 degrees
(b) 180 degrees
(c) 270 degrees
(d) Greater than 180 degrees
Ans: (d)
In spherical geometry, the sum of the angles in a triangle is always greater than 180 degrees. This is because the surface of a sphere is curved, and the geometry on a sphere differs from that of a flat plane.

Q5: Which type of geometry finds its application in topology?
(a) Euclidean Geometry
(b) Spherical Geometry
(c) Hyperbolic Geometry
(d) Analytical Geometry
Ans: (c)
Hyperbolic geometry is the type of geometry that finds its application in topology, which is the study of properties preserved through continuous transformations. Hyperbolic geometry deals with the geometry of curved surfaces and has applications in various fields, including physics and computer science.

Short Questions

Q1: Define Euclidean Geometry.
Ans: Euclidean Geometry is the branch of geometry that studies the properties and relationships of plane and solid figures based on Euclid's axioms and postulates. It involves concepts such as points, lines, angles, polygons, circles, and three-dimensional shapes.

Q2: State two of Euclid's axioms in geometry.
Ans: Euclid's axioms are assumptions or postulates that form the foundation of Euclidean Geometry. These axioms are accepted without proof and are used to establish logical deductions in geometry.

Q3: What are the three types of plane shapes in geometry? Give examples of each.
Ans:

• Polygons: Polygons are closed curves made up of straight line segments. Examples include triangles, quadrilaterals (e.g., square, rectangle), pentagons, and hexagons.
• Circles: A circle is a closed curve consisting of all points equidistant from a central point. It has no edges or corners. Examples include a wheel, a coin, or the cross-section of a cylindrical object.
• Lines: Lines are one-dimensional figures that extend infinitely in both directions. They have no endpoints. Examples include a straight line on a paper, a line drawn on a road, or the edge of a ruler.

Q4: What are the basic components of planes in geometry?
Ans: The basic components of planes in geometry are points, lines, and angles.

• Points: Points are the basic units of geometry and have no dimensions. They are represented by a dot.
• Lines: Lines are sets of points that extend infinitely in two opposite directions. They have length but no width or thickness.
• Angles: Angles are formed when two lines intersect or when lines meet at a point. They measure the amount of rotation between the lines.

Q5: Explain the concept of direction cosines in three-dimensional geometry.
Ans: Direction cosines in three-dimensional geometry are the cosines of the angles that a line makes with the positive x-axis, y-axis, and z-axis. They are denoted as l, m, and n, respectively. The direction cosines provide information about the orientation of a line in space and can be used to determine angles between lines, projections, and various geometric calculations. The direction cosines satisfy the condition l^2 + m^2 + n^2 = 1, which ensures that they lie on the unit sphere.

Fill in the blanks

1. Euclidean geometry is primarily concerned with the shapes and sizes of __________.
Ans: objects

2. Euclidean geometry is based on __________ and __________.
Ans: axioms, theorems

3. The fundamental concepts of Euclidean geometry include Points and Lines, Euclid's Axioms and Postulates, Geometrical Proof, and __________.
Ans: Euclid's Fifth Postulate

4. The fifth postulate of Euclidean Geometry states that any two straight lines are __________ parallel that are equidistant from one another at two points.
Ans: infinitely

5. Euclid's axioms are based on assumptions and have __________ proof for them.
Ans: no

Match the column

Ans: 

True or False

1. Euclidean geometry is primarily concerned with the shapes and sizes of objects. (True/False)
Ans: True

2. Euclidean geometry is based on postulates and theorems. (True/False)
Ans: True

3. Euclid's axioms are universally accepted and have proofs for them. (True/False)
Ans: False

4. Spherical geometry is the study of geometry on a curved surface. (True/False)
Ans: True

5. Plane geometry involves the study of geometry in a plane. (True/False)
Ans: True