CBSE Class 9 Mathematics Introduction to Euclid's Geometry MCQs Set 04

Answer: (b) only one

Explanation:
1. Euclid's axiom: given two distinct points, there is one and only one line containing both.
2. So exactly one line passes through them.

Teacher's Note:
1. Two points fix the line.
2. This is the basis of drawing a line with a ruler.

Answer: (c) one

Explanation:
1. Two distinct lines cannot have more than one point in common.
2. So the largest number is one.

Teacher's Note:
1. If they had two points in common they would be the same line.
2. Parallel lines meet in no point.

Answer: (a) True

Explanation:
1. Point, line and plane are the basic undefined terms of geometry.
2. So the statement is true.

Teacher's Note:
1. These terms are explained but not defined.
2. Recall the definitions and axioms of Euclid's geometry.

Answer: (b) False

Explanation:
1. A line is one of the basic undefined terms of geometry.
2. So the statement is false.

Teacher's Note:
1. Point, line and plane are undefined.
2. Recall the definitions and axioms of Euclid's geometry.

Answer: (d) True

Explanation:
1. Given two distinct points there is exactly one line through them.
2. So the statement is true.

Teacher's Note:
1. This is one of Euclid's axioms.
2. Recall the definitions and axioms of Euclid's geometry.

Answer: (b) True

Explanation:
1. The two end points fix the segment, and its length is the distance between them.
2. So the statement is true.

Teacher's Note:
1. A segment is a terminated part of a line.
2. Recall the definitions and axioms of Euclid's geometry.

Answer: (c) point, line and plane

Explanation:
1. Point, line and plane are accepted without formal definition.
2. All other terms are defined using them.

Teacher's Note:
1. Euclid's attempt to define them used other undefined words.
2. They are the basic concepts.

Answer: (a) infinitely many

Explanation:
1. All lines through P other than the one parallel to AB meet AB.
2. There are infinitely many lines through P, so infinitely many are not parallel to AB.

Teacher's Note:
1. Count all lines through P, then remove the parallel one.
2. One line is removed from an infinite set.

Answer: (b) parallel to each other

Explanation:
1. Two lines parallel to the same line are parallel to each other.
2. So \( AB\parallel CD \).

Teacher's Note:
1. This is a standard axiom of parallel lines.
2. The distance relationship is transitive.

Answer: (c) three

Explanation:
1. The pairs of points are AB, BC and CA.
2. Each pair gives one line, so three lines.

Teacher's Note:
1. Count the pairs of points.
2. There are three pairs.

Answer: (d) one

Explanation:
1. All three points lie on a single line.
2. Two points fix the line and the third lies on it, so only one line contains all three.

Teacher's Note:
1. Collinear means lying on the same line.
2. Any two of them fix that line.

Answer: (b) a straight line may be drawn from any one point to any other point

Explanation:
1. The first postulate lets us join any two points by a straight line.
2. The other options are the fourth, third and second postulates respectively.

Teacher's Note:
1. Recall the five postulates in order.
2. It is the basis of joining two points with a ruler.

Answer: (c) all right angles are equal to one another

Explanation:
1. The fourth postulate fixes a standard for angles.
2. It says every right angle has the same measure.

Teacher's Note:
1. It is about angles, not lines or circles.
2. Right angles are all \( 90^\circ \).

Answer: (d) third postulate

Explanation:
1. The first joins two points, the second extends a segment, and the third gives circles.
2. So it is the third postulate.

Teacher's Note:
1. Order the postulates by what they construct.
2. Circles come after lines.

Answer: (b) Euclid

Explanation:
1. Euclid, a Greek mathematician, systematised geometry in his work.
2. He is therefore called the Father of Geometry.

Teacher's Note:
1. The Elements was written by Euclid.
2. The name geometry means measuring the earth.

Answer: (c) earth and measure

Explanation:
1. 'Geo' means earth and 'metron' means measure.
2. So geometry means measurement of the earth.

Teacher's Note:
1. Geometry began with land measurement.
2. Geo = earth.

Answer: (a) that which has no part

Explanation:
1. The first definition: a point is that which has no part.
2. A line has length only and a surface has length and breadth only.

Teacher's Note:
1. A point has no size.
2. Compare with the definitions of line and surface.

Answer: (b) they lie on a single line

Explanation:
1. Collinear points have a line containing all of them.
2. Concurrent lines, by contrast, pass through a common point.

Teacher's Note:
1. Co-linear means on one line.
2. Do not confuse with concurrent lines.

Answer: (c) there is a point lying on all of them

Explanation:
1. Concurrent lines pass through a common point.
2. For example the three medians of a triangle meet at one point.

Teacher's Note:
1. Concurrent lines meet at a point.
2. Parallel lines never meet.

Answer: (d) they are collinear and A is their only common point

Explanation:
1. Opposite rays lie on one line and start at the same point A going in opposite directions.
2. A is then their only common point.

Teacher's Note:
1. Opposite rays together form a line.
2. They make a straight angle at A.

Answer: (c) their lengths are equal

Explanation:
1. Segments are congruent when one can be superposed exactly on the other.
2. This happens exactly when they have equal lengths.

Teacher's Note:
1. Congruent means identical in size.
2. Position does not matter.

Answer: (d) the length of the line segment PQ

Explanation:
1. The distance is measured along the straight segment joining the points.
2. It is the shortest path between them.

Teacher's Note:
1. Distance means straight-line length.
2. A ray has no fixed length.