CBSE Class 6 Mathematics Basic Geometrical Concepts Worksheet Set 03

Chapter -4: Basic Geometrical Ideas

Q1. Fill in the blanks.

Question 1.1. A line is made up of __________ points.
Answer: infinite (or countless)
In simple words: A line extends endlessly in both directions and contains an infinite number of points.

Exam Tip: Remember that a line has no endpoints and is a collection of infinitely many points.

Question 1.2. In a line segment XY, the points X & Y are called the _________ points of the segments.
Answer: end
In simple words: The two fixed points that bound a line segment are its endpoints.

Exam Tip: Unlike lines and rays, line segments always have two definite endpoints.

Question 1.3. The ray AB, A is called the________.
Answer: initial point (or starting point)
In simple words: The fixed point from which a ray starts is called its initial point.

Exam Tip: In notation like ray AB, the first letter always denotes the starting point.

Question 1.4. One & the only one line can be drawn through _________ points.
Answer: two given distinct
In simple words: Exactly one straight line passes through any two given distinct points.

Exam Tip: This is a fundamental postulate of geometry: two points determine a unique line.

Question 1.5. _________lines do not intersect each other.
Answer: Parallel
In simple words: Parallel lines remain at the same distance apart and never meet, no matter how far they are extended.

Exam Tip: Parallel lines have no common points of intersection.

Question 1.6. The curve which does not cross itself is called _________.
Answer: a simple curve
In simple words: A curve that does not intersect itself anywhere is a simple curve.

Exam Tip: Distinguish carefully between simple curves and curves that cross over themselves.

Question 1.7. A closed figure made up of line segments is called a __________.
Answer: polygon
In simple words: A polygon is a closed two-dimensional shape formed entirely of straight line segments.

Question 1.8. A polygon with the least no. of sides is called a __________.
Answer: triangle
In simple words: A triangle has 3 sides, which is the minimum number of sides needed to enclose a space with straight lines.

Exam Tip: A polygon cannot be formed with fewer than 3 sides.

Q2. Looking at the given figure, fill in the blanks.

Question 2.1. AB is the _______ of the circle.
Answer: chord
In simple words: A line segment joining any two points on a circle is a chord.

Exam Tip: Any line segment with both endpoints on the circle is classified as a chord.

Question 2.2. OL is the _______ of the circle.
Answer: radius
In simple words: The distance from the center O to any point L on the circle is the radius.

Exam Tip: A radius connects the center of the circle to any point on its boundary.

Question 2.3. AC is the _______ of the circle.
Answer: diameter
In simple words: A chord passing directly through the center of the circle is the diameter.

Exam Tip: The diameter is the longest chord and equals twice the radius (\(d = 2r\)).

Question 2.4. Chords EF & AB are _______.
Answer: chords (or line segments)
In simple words: Both EF and AB connect two points on the circle, making them chords.

Question 2.5. ________ the longest chord of the circles. (Diameter is...)
Answer: Diameter is
In simple words: The diameter is always the longest possible chord in any circle.

Exam Tip: Remember that diameter passes through the center, maximizing the distance between two points on the circle.

Question 2.6. Radius is ______ the length of the diameter of a circle.
Answer: half (\(\frac{1}{2}\))
In simple words: The radius is exactly half the length of the diameter.

Exam Tip: Formula relationship: \(\text{Radius} = \frac{\text{Diameter}}{2}\).

Question 2.7. The length of the boundary of a circle is called its ________.
Answer: circumference
In simple words: Circumference is the special term for the perimeter or boundary length of a circle.

Exam Tip: Circumference formula is \(C = 2\pi r\).

Question 2.8. _________ is a part of the circle. (Arc)
Answer: An arc
In simple words: Any connected section of the circle boundary is an arc.

Exam Tip: Arcs can be minor or major depending on their length relative to the semicircle.

Question 2.9. _________ is the segment of the circle. (Region bounded by chord and arc)
Answer: A segment
In simple words: The region enclosed by a chord and an arc is called a segment of the circle.

Question 2.10. _________ is the sector of the circle.
Answer: A sector
In simple words: The region bounded by two radii and an arc is called a sector.

Exam Tip: Think of a sector like a slice of pizza or pie.

Q3. Answer the following questions based on the given figure.

Question 3.1. \(\angle XOY\) is an _________.
Answer: angle (or straight angle / geometric angle)
In simple words: \(\angle XOY\) forms an angle with vertex O.

Exam Tip: An angle is formed by two rays sharing a common endpoint.

Question 3.2. ________ is the vertex of \(\angle XOY\).
Answer: O
In simple words: The common endpoint where the two rays meet is vertex O.

Question 3.3. OX & OY are called the ________.
Answer: arms (or sides) of the angle
In simple words: The rays forming the angle are its arms.

Exam Tip: Every angle consists of two arms and one vertex.

Question 3.4. ____,____,____ & ____ are the points on the \(\angle XOY\). (Based on standard ray points O, F, P, Y)
Answer: O, F, P, Y
In simple words: These points lie along the arms or boundary of the angle figure.

Exam Tip: Points lying directly on the rays forming the angle are points on the angle.

Question 3.5. The point _______ lie on the interior of \(\angle XOY\).
Answer: D
In simple words: Point D is located inside the region bounded by the arms of the angle.

Exam Tip: Interior points lie strictly between the two arms of the angle.

Question 3.6. The points _______ & _______ are the exterior of \(\angle XOY\).
Answer: E, K (or E and any exterior point)
In simple words: Points E and K lie outside the region of the angle.

Exam Tip: Exterior points lie outside the region enclosed by the angle's arms.

Q4. From the figure, name :

Question 4(a). Four rays :- _______________________.
Answer: Ray XA, Ray XB, Ray XC, Ray XD
In simple words: The four rays starting from the intersection point X are XA, XB, XC, and XD.

Exam Tip: Always start naming a ray from its initial vertex point.

Question 4(b). Eight triangles :- _____________________.
Answer: Triangle ABE, Triangle ADE, Triangle BCE, Triangle CDE, Triangle ABC, Triangle ADC, Triangle ABD, Triangle BCD
In simple words: The composite star-like rhombus figure contains 8 distinct triangles formed by combining smaller triangular sections around center E.

Exam Tip: Systematically list triangles by examining the inner quadrants and outer triangular regions.

Question 4(c). 8 pairs of adjacent side - _____________
Answer: (AB, BH), (BH, HA), (HA, AG), (AG, GF), (GF, FE), (FE, ED), (ED, DC), (DC, CB) (and corresponding cyclic combinations)
In simple words: Adjacent sides share a common vertex point on the polygon boundary.

Exam Tip: Adjacent sides meet at a common corner vertex.

Question 4(d). 8 pairs of adjacent vertices - __________.
Answer: (A, B), (B, H), (H, G), (G, F), (F, E), (E, D), (D, C), (C, A) (connected consecutively along the perimeter)
In simple words: Adjacent vertices are endpoints connected directly by a side of the polygon.

Exam Tip: Look at consecutive corner points along the outer boundary.