CBSE Class 6 Mathematics Basic Geometrical Concepts Worksheet Set 11

Basic Geometrical Ideas

Question 1. Fill in the blanks, using the figure given alongside
a. The point of intersection of the line segments AB and BC is ______.
b. The common arm of \(\angle 1\) and \(\angle 2\) is __________.
c. \(\angle 4\) can be renamed using 3 letters as _______ and ________.
d. ________ is the diagonal of quadrilateral ABCD.

Answer:
a. B
b. AC
c. \(\angle DAB\), \(\angle BAD\)
d. AC
In simple words: We identify points, line segments, angles, and diagonals using the labeled vertices in the given polygon.

Exam Tip: When naming an angle with three letters, always ensure the vertex letter is in the middle (e.g., \(\angle BAD\)).

Question 2. State whether the statements are true (T) or false (F).
a. Only one ray can be drawn with a given initial point.
b. A line is longer than a line segment.
Answer:
a. False (F) - Infinitely many rays can be drawn originating from a single fixed initial point in different directions.
b. False (F) - A line extends endlessly in both directions, and a line segment has a fixed length, but comparison of length only applies to figures with finite lengths (like line segments). A line has infinite length, so we cannot strictly say one is "longer" than another in a measurable numerical sense.
In simple words: A single point can start countless rays, and lines are infinite so they cannot be compared by standard length.

Exam Tip: Remember that a line has no endpoints and infinite length, whereas a line segment has two fixed endpoints.

Question 3. Choose the correct alternative:-
i. A quadrilateral is a simple closed figure formed by ____ line segments.
(a) 3
(b) 4
(c) 2
(d) 5
Answer: (b) 4
A quadrilateral is defined as a four-sided polygon, which means it is bounded by four line segments.
In simple words: Quad means four, so a quadrilateral has four sides.

Exam Tip: Memorize polygon name prefixes: tri- (3), quad- (4), penta- (5), hexa- (6).

Question 3(ii). Which of the following has no end point?
(a) \(\overleftrightarrow{AB}\)
(b) \(\overline{CD}\)
(c) \(\overline{BC}\)
(d) \(\overline{EF}\)
Answer: (a) \(\overleftrightarrow{AB}\)
A line denoted with arrows on both ends (\(\overleftrightarrow{AB}\)) extends infinitely in both directions and has no endpoints, whereas line segments (\(\overline{CD}\), \(\overline{BC}\), \(\overline{EF}\)) have two definite endpoints.
In simple words: Lines go on forever without ending, while line segments stop at two points.

Exam Tip: Look closely at the notation above the letters: arrows indicate a line, dots or plain bars indicate a line segment.