Euclid's Geometry - Free MCQ Practice Test with solutions, Class 9 Maths

The line from the centre of a circle to any point on its edge is called the radius.

Here is why:

• The radius is a line connecting the circle's centre to its circumference.
• It is half the length of the diameter.
• This is a fundamental concept in geometry.

Theorems are statements that are proven using various components:

• Definitions provide the fundamental concepts needed for understanding.
• Axioms are accepted truths used as a starting point for further reasoning.
• Previously proved statements build upon known truths.
• Deductive reasoning ensures logical consistency from premises to conclusion.

The relationship between the whole and the part is straightforward:

• In any scenario involving a whole and its part, the whole is always greater than the part.
• This means that if W represents the whole and P represents a part, then W > P.

When three points are collinear, they all lie on the same straight line.Therefore, with three collinear points, we can only create one line segment using all three points. 

The number of points that can lie on a line is innumerable. Here's why:

• A line is defined as a straight one-dimensional figure extending infinitely in both directions.
• It contains an infinite number of points along its length.
• The concept of infinity means there is no limit to the number of points.

Therefore, the correct understanding is that a line can host infinitely many points.

 According to the definition of parallel lines “lines are parallel if they do not intersect”. They are not intersecting. Definition: a statement that gives the exact meaning of the given word. Hence, 'lines are parallel if they do not intersect' is stated in the form of definition.

Things which are double of the same things are equal to one another.
Example : 
1. If 2x = 2y then x = y.
2. If a = b, then 2a = 2b

If three points A, B, and C are distinct and B lies on line AC, then:

• Line segment AB is part of line segment AC.
• Line segment BC is also part of line segment AC.

If AB + BC = AC, then:

• Since B is on the line between A and C, AB must be less than AC.
• Therefore, AB < AC is the correct statement.

The correct answer is C: infinite.

Here's why:
- In geometry, through a single point, an infinite number of lines can pass.
- This concept is a fundamental property of Euclidean geometry.
- Imagine a point as the intersection of multiple lines, where each line extends infinitely in both directions.
- Therefore, the correct answer is that an infinite number of lines can pass through a single point.

In Euclidean geometry, the relationship between parallel lines is governed by the transitive property. This means that:

• If two lines are both parallel to a third line, they must also be parallel to each other.
• Since intersecting lines are not parallel, they cannot both be parallel to another common line.
• Therefore, two intersecting lines cannot be parallel to a single common line.

A theorem is a statement that has been proven to be true based on previously established statements, such as other theorems, and generally accepted principles like axioms and postulates.

• A definition explains the meaning of a term or concept.
• A postulate is a statement assumed to be true without proof.
• An axiom is a fundamental truth accepted without proof.

As such, a proof is required for theorems, not for definitions, postulates, or axioms.

If P lies between M and N, and C is the midpoint of MP, then the following holds true:

• MC + CN = MN

This is because:

• C divides MP into two equal parts.
• The segment from M to C plus the segment from C to N equals the entire segment MN.

• The edges of a surface are defined by lines where two surfaces meet.
• Plans refer to flat surfaces, not edges.
• Points are the smallest units in geometry but do not define edges.
• Rays extend infinitely in one direction, but do not represent edges.
• Thus, lines, which are made up of multiple points, are the correct representation of edges of a surface.

Euclid’s first postulate states that “A straight line may be drawn from any one point to any other point.”

• Option (a) matches exactly with this definition.

• Option (b) actually states Euclid’s third postulate, not the first.

• Option (c) is Euclid’s fourth postulate.

• Option (d) is not one of Euclid’s postulates but a property of intersecting lines.

✅ Hence, (a) is correct.

A solid has shape, size, position and can be moved from one place to another. So, solid has three dimensions

 A point is that which has no part i.e., no length, no breadth and no height. So, it has no dimension.

 Boundaries of a solid are called surfaces. A surface (plane) has only length and breadth. So, it has two dimensions.

Euclid's second postulate states:

• A terminated line can be extended indefinitely.

This means that if you have a line segment, you can keep extending it in either direction without any limit.