Chapter Exam

Chapter 5 MATHS : Introduction to Euclid's Geometry — Online MCQ Test

Q: According to Euclid, which of the following is considered a 'dimensionless' entity?

Answer: A. A point — Euclid defined a point as that which has no part; hence it has no length, breadth, or height (dimension).

Q: The boundaries of surfaces are:

Answer: C. Lines — According to Euclid's definitions, the boundaries of surfaces are lines.

Q: If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side. This is:

Answer: C. Euclid's fifth postulate — This statement is the famous fifth postulate of Euclid, also known as the Parallel Postulate.

Q: Consider two lines L1 and L2. If a transversal intersects them such that the sum of interior angles on one side is 180 degrees, the lines must be:

Answer: B. Parallel — According to the Playfair's axiom (a variation of Euclid's 5th postulate), if the interior angles sum to 180 degrees, they do not meet, meaning they are parallel.

MATHS · CLASS 9th · Andhra State Board

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Chapter 5 MATHS : Introduction to Euclid's Geometry — Important Questions & Answers (FAQ)

Frequently asked questions from Andhra State Board CLASS 9th MATHS — Chapter 5 MATHS : Introduction to Euclid's Geometry, with answers and explanations. These are sample questions; the exam has its own separate question set.

According to Euclid, which of the following is considered a 'dimensionless' entity?

A. A point ✓
B. A line
C. A plane
D. A solid

Answer: A. A point
Euclid defined a point as that which has no part; hence it has no length, breadth, or height (dimension).

The boundaries of surfaces are:

A. Points
B. Curves
C. Lines ✓
D. Surfaces

Answer: C. Lines
According to Euclid's definitions, the boundaries of surfaces are lines.

If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side. This is:

A. Euclid's first axiom
B. Euclid's second postulate
C. Euclid's fifth postulate ✓
D. Euclid's fourth postulate

Answer: C. Euclid's fifth postulate
This statement is the famous fifth postulate of Euclid, also known as the Parallel Postulate.

Consider two lines L1 and L2. If a transversal intersects them such that the sum of interior angles on one side is 180 degrees, the lines must be:

A. Intersecting
B. Parallel ✓
C. Perpendicular
D. Coincident

Answer: B. Parallel
According to the Playfair's axiom (a variation of Euclid's 5th postulate), if the interior angles sum to 180 degrees, they do not meet, meaning they are parallel.

If 'a' and 'b' are two distinct lines, and they intersect at a point P, can there be another point Q such that 'a' and 'b' both pass through Q?

A. Yes
B. No, because two distinct lines can intersect at only one point. ✓
C. Only if the lines are parallel.
D. Only if the lines are the same.

Answer: B. No, because two distinct lines can intersect at only one point.
Euclid's geometry establishes that two distinct lines can have at most one point in common.