CBSE Class 6 Mathematics Basic Geometrical Concepts Worksheet Set 02

Question 1. Two distinct lines meet at a point is called _____
(a) parallel lines
(b) intersecting lines
(c) perpendicular lines
(d) none of the options
Answer: (b) intersecting lines
When two or more lines cross or meet each other at a common point, they are called intersecting lines, and the common point is known as the point of intersection.
In simple words: Lines that cross each other at a single point are intersecting lines.

Exam Tip: Remember that parallel lines never meet, whereas intersecting lines always share one common point.

Question 2. How many lines can pass through 2 given points?
(a) many
(b) 2
(c) 3
(d) 1
Answer: (d) 1
According to the fundamental axiom of geometry, exactly one straight line can be drawn to pass through two distinct given points.
In simple words: Only one straight line can connect any two points.

Exam Tip: Keep this basic geometric postulate in mind: two points determine a unique line.

Question 3. If a curve does not cross itself, then it is called _____
(a) simple curve
(b) open curve
(c) diagonal
(d) none of the options
Answer: (a) simple curve
A simple curve is defined as a curve that does not cross or intersect its own path anywhere between its endpoints.
In simple words: A curve that never intersects itself is a simple curve.

Exam Tip: Do not confuse a simple curve with a closed curve; a simple curve can be either open or closed as long as it does not cross itself.

Question 4. The line segment joining the two non-consecutive vertices is called _____
(a) ray
(b) angle
(c) diagonal
(d) none of the options
Answer: (c) diagonal
A diagonal of a polygon is a line segment that connects two non-consecutive (non-adjacent) vertices of the polygon.
In simple words: Connecting opposite corners of a shape with a line segment gives a diagonal.

Exam Tip: Consecutive vertices share a side, whereas non-consecutive vertices are opposite each other and form diagonals when connected.

Question 5. There are _____ diagonals in a rectangle.
(a) 0
(b) 2
(c) 3
(d) 4
Answer: (b) 2
A rectangle has 4 vertices. By joining the opposite non-consecutive vertices, we get 2 equal diagonals.
In simple words: A rectangle always has 2 diagonals.

Exam Tip: The two diagonals of a rectangle are always equal in length and bisect each other.

Question 6. Which of the following is not a polygon?
(a) square
(b) triangle
(c) rectangle
(d) circle
Answer: (d) circle
A polygon is a closed figure bounded by three or more straight line segments. A circle is a curved figure, not made of line segments, hence it is not a polygon.
In simple words: Polygons are made of straight lines, but circles are curved.

Exam Tip: Always check if a closed shape is bounded exclusively by line segments to determine if it is a polygon.

Question 7. The meeting point of a pair of sides is called _____
(a) side
(b) vertex
(c) region
(d) angle
Answer: (b) vertex
The point where two sides (or line segments) of a polygon meet is known as a vertex.
In simple words: The corner point where two sides meet is a vertex.

Exam Tip: Plural of vertex is vertices. A polygon has an equal number of sides and vertices.

Question 8. The end points of the same side of a polygon are called _____
(a) adjacent sides
(b) adjacent vertices
(c) diagonals
(d) adjacent angles
Answer: (b) adjacent vertices
The two endpoints that lie on the same side of a polygon are adjacent to each other and are called adjacent vertices.
In simple words: Vertices at the two ends of the same side are adjacent vertices.

Exam Tip: Adjacent vertices form the endpoints of a single side of the polygon.

Question 9. A region in the interior of a circle enclosed by a chord and an arc is called _____
(a) segment
(b) sector
(c) circumference
(d) diameter
Answer: (a) segment
The area bounded by a chord and the arc intercepted by it is called a segment of the circle.
In simple words: The slice of a circle between a chord and its arc is a segment.

Exam Tip: Do not confuse segment with sector; a sector is enclosed by two radii and an arc, while a segment is enclosed by a chord and an arc.

Question 10. The _____ divide a circle into two semi-circles
(a) sector
(b) diameter
(c) radius
(d) segment
Answer: (b) diameter
A diameter is the longest chord passing through the center of a circle, and it divides the circle into two equal halves called semi-circles.
In simple words: A diameter cuts a circle right in half into two semi-circles.

Exam Tip: The diameter is always twice the length of the radius (\(d = 2r\)).

Question 11. Name all the 3 angles, sides and vertices of the triangle ABC. Name the side opposite to vertex A.
Answer:
- Angles: \(\angle ABC\), \(\angle BCA\), \(\angle CAB\)
- Sides: AB, BC, CA
- Vertices: A, B, C
- Side opposite to vertex A: BC
In simple words: Identify all corners, sides, and angles of triangle ABC based on standard geometric naming conventions.

Exam Tip: When naming an angle, the vertex letter must always be written in the middle.

Question 12. Draw a circle of radius 4 cm and mark the following.
a) A Sector
b) A Chord
c) Two Radii
d) A Segment
e) An Arc
f) A Diameter
g) Two points in the interior and two points in the exterior
Answer:
Construction steps:
1. Open the compass to a radius of 4 cm using a ruler.
2. Mark a point O as the center and draw the circle.
3. Label center O, radii OA and OB, chord CD, arc AB, sector AOB, segment formed by chord CD, diameter through center, interior points P and Q, and exterior points X and Y.
In simple words: Draw a circle with a 4 cm radius and label all requested parts inside and around it.

Exam Tip: Always set your compass correctly against a scale before drawing the circle.

Question 13. From the figure, name the following.
a) Two pairs of opposite angles.
b) Two pairs of opposite sides.
c) All pairs of adjacent angles.
d) All pairs of adjacent sides
Answer:
For quadrilateral PQRS:
a) Two pairs of opposite angles: \(\angle P\) and \(\angle R\), \(\angle Q\) and \(\angle S\)
b) Two pairs of opposite sides: PQ and SR, PS and QR
c) All pairs of adjacent angles: (\(\angle P, \angle Q\)), (\(\angle Q, \angle R\)), (\(\angle R, \angle S\)), (\(\angle S, \angle P\))
d) All pairs of adjacent sides: (PQ, QR), (QR, RS), (RS, SP), (SP, PQ)
In simple words: Identify opposite and adjacent sides, angles, and vertices of quadrilateral PQRS.

Exam Tip: Opposite angles and sides do not share a common vertex or side.

Question 14. From the given figure, identify
a) all line segments
b) all the vertices
c) all the diagonals
Answer:
For the given hexagon ABCDEF with center O:
a) All line segments: AB, BC, CD, DE, EF, FA, AO, BO, CO, DO, EO, FO, AC, AD, AE, BD, BE, BF, CE, CF, DF (and internal intersecting segments).
b) All vertices: A, B, C, D, E, F, O
c) All diagonals: AC, AD, AE, BD, BE, BF, CE, CF, DF (and main hexagon diagonals AD, BE, CF)
In simple words: List every individual line segment, corner point vertex, and diagonal in the figure.

Exam Tip: Systematic naming starting alphabetically prevents missing any line segments or diagonals.

Question 15. How many line segments are there in the adjoining figure.
Answer:
Counting all distinct visible line segments in the rectangle ABCD with internal segments:
- Outer rectangle sides: AB, BC, CD, DA (4 segments)
- Internal segments: AE, BE, CE, DE, FG, BF, CG, etc.
Total distinct line segments = 15
In simple words: Count all individual straight line segments making up the entire geometric figure.

Exam Tip: Break down complex figures into triangles and rectangles to count line segments accurately without repetition.

Question 16. From the given quadrilateral KLMN, Name a) 8 triangles b) 2 diagonals
Answer:
a) 8 triangles formed around center O and vertices: \(\triangle OKN\), \(\triangle ONM\), \(\triangle OML\), \(\triangle OLK\), \(\triangle KNM\), \(\triangle NML\), \(\triangle MLK\), \(\triangle LKN\)
b) 2 diagonals: KM and LN
In simple words: Identify the 8 smaller and combined triangles meeting at the center O, and the 2 main diagonals.

Exam Tip: Diagonals intersecting at the center create multiple smaller triangles sharing vertex O.

Question 17. In the given figure, mention the name of
a) Any two pairs of intersecting lines.
b) Any 4 line segments
c) Any 4 rays
d) Line passing through B
e) Line on which D lies
f) Two non-intersecting line segments
Answer:
a) Two pairs of intersecting lines: Line AB and Line MN, Line CD and Line EF
b) Any 4 line segments: AB, CD, EF, GH
c) Any 4 rays: OA, OB, OC, OD
d) Line passing through B: Line AB (or line containing B and C)
e) Line on which D lies: Line CD (or line containing D and O)
f) Two non-intersecting line segments: AB and EF (or parallel segments if applicable)

In simple words: Identify specific geometric elements like lines, rays, segments, and points from the intersecting line diagram.

Exam Tip: Understand the difference in notation: a line has arrows on both ends, a ray has one endpoint and extends infinitely in one direction, and a line segment has two fixed endpoints.