GSEB Class 6 Maths Solutions Chapter 4 ભૂમિતિના પાયાના ખ્યાલો InText Questions

Try This [Page Number 70]

Question 1. Show four points on paper with a pencil tip and label them with the letters A, C, P, H. Name these points in different ways. One of them can also be shown like this: P. H. C.
Answer: We can show four points in different ways as given below:
(1) C D E F
(2) L M N
(3) R
(4) D L
P M N P Pi
In simple words: Draw four dots on paper using a pencil. Give each dot a letter like A, C, P, H. There are many ways to write down what these dots are called, for example, P, H, C.

Exam Tip: When naming points, ensure each point is distinct and uses appropriate capital letters.

Find Out.

Answer:

Events Observed In Our Daily Life:
1. The point of a ballpen gives the idea of a point.
2. The tip of a pencil gives the idea of a point.
3. The sharp end of a compass gives the idea of a point.
4. The head of a pin gives the idea of a point.
In simple words: Look around in your daily life. Things like the tip of a pen, a pencil point, a compass needle, or a pin's head are all good examples of a mathematical point.

Exam Tip: Always relate mathematical concepts to real-life examples to better understand and remember them.

Try This [Page Number 71]

Question 1. In the figure, the names of the line segments are shown. Is A the endpoint of every line segment?
Answer: In the figure, line segments AB and AC are shown. Point A is a common endpoint for both line segment AB and line segment AC. Therefore, yes, point A is the endpoint of every line segment in this specific figure.
In simple words: The picture shows lines AB and AC. Point A is where both lines end. So, yes, A is the end for both of them in this drawing.

Exam Tip: Identify common points and endpoints carefully in diagrams involving line segments or rays.

Do This: [Page Number 72]

Question. Take a sheet of paper. Fold it in a way that gives the idea of intersecting lines, and discuss the following:
(a) Can these two lines intersect at more than one point?
(b) Can more than two lines intersect at one point?
Answer:
(a) When we take a sheet of paper and fold it, first horizontally and then vertically, we get the idea of two lines. These two lines intersect each other at one and only one point. Paper folding demonstrates this clearly. So, two distinct lines can intersect at only one point.
(b) Yes, more than two lines can intersect at one point. If we take a paper sheet and fold it multiple times to create many folds, these many lines can all pass through a single common point. For instance, in the figure on the next page, lines \(l\), \(m\), \(p\), and \(q\) all intersect at a common point O.
In simple words: For (a), two straight lines can only cross each other at one place. They can't meet more than once. For (b), yes, many lines can all cross through the same single point, like spokes on a wheel.

Exam Tip: Remember that two distinct straight lines can intersect at most at one point. However, multiple lines can converge and pass through a single common point.

Think, Discuss, And Write [Page Number 74]

Question. Assume that \( \overrightarrow{\mathbf{P Q}} \) is a ray.
(a) What is its starting point/origin?
(b) Where is point Q located on the ray?
(c) Can we say that Q is the starting point of the ray?
Answer:
(a) The starting point, or origin, of ray \( \overrightarrow{\mathbf{P Q}} \) is point P.
(b) Point Q is located on ray \( \overrightarrow{\mathbf{P Q}} \), away from point P.
(c) No, we cannot say that Q is the starting point of ray \( \overrightarrow{\mathbf{P Q}} \). The starting point of ray \( \overrightarrow{\mathbf{P Q}} \) is point P.
In simple words: For (a), the ray starts at P. For (b), Q is a point on the ray, further along from P. For (c), no, Q is not the start point; P is the start point.

Exam Tip: A ray always has a definite starting point (origin) and extends infinitely in one direction. The notation \( \overrightarrow{AB} \) indicates that the ray starts at A and passes through B.

Try This [Page Number 74]

Question 1. Name the rays given in the figure.
Question 2. Is T the starting point of every given ray?
Answer: We know that a ray is part of a line. A ray originates from an endpoint and extends infinitely in one direction.
1. In the given figure above, there are four rays. These four rays are \( \overrightarrow{\mathrm{TA}} \), \( \overrightarrow{\mathrm{TN}} \), \( \overrightarrow{\mathrm{NB}} \), and \( \overrightarrow{\mathrm{TB}} \).
2. T is not the origin of all the above rays. T is the origin only for rays \( \overrightarrow{\mathrm{TA}} \), \( \overrightarrow{\mathrm{TN}} \), and \( \overrightarrow{\mathrm{TB}} \). The ray \( \overrightarrow{\mathrm{NB}} \) has N as its origin, not T.
In simple words: For Question 1, the picture shows these rays: \( \overrightarrow{\mathrm{TA}} \), \( \overrightarrow{\mathrm{TN}} \), \( \overrightarrow{\mathrm{NB}} \), and \( \overrightarrow{\mathrm{TB}} \). For Question 2, T is only the start for some rays, not all of them. For example, \( \overrightarrow{\mathrm{NB}} \) starts at N, not T.

Exam Tip: Correctly identifying the starting point (origin) is crucial when naming rays, as it defines the direction of the ray.

Do This: [Page Number 77]

Question. Try to make polygons using the following:
(1) With five matchsticks
(2) With four matchsticks
(3) With three matchsticks
(4) With two matchsticks, in what state is it not possible? Why?
Answer:
(1) With five matchsticks, a pentagon can be formed.

(2) With four matchsticks, a quadrilateral (like a square) can be formed.

(3) With three matchsticks, a triangle can be formed.

(4) A polygon is a closed figure that is enclosed by line segments. With the use of only two matchsticks, it is not possible to create a closed figure.
In simple words: For (1), five sticks make a five-sided shape (pentagon). For (2), four sticks make a four-sided shape (quadrilateral). For (3), three sticks make a three-sided shape (triangle). For (4), you can't make a closed shape with just two sticks because a polygon needs at least three sides to be closed.

Exam Tip: Remember that a polygon is defined as a closed figure made up of three or more line segments. This is why a minimum of three matchsticks is needed.

HOTs Type Questions And Answers

Question 1. The length of _______ can be measured.
(a) \( \overrightarrow{\mathrm{PO}} \)
(b) \( \overrightarrow{\mathrm{XY}} \)
(c) \( \overrightarrow{\mathrm{RM}} \)
(d) \( \overrightarrow{\mathrm{GD}} \)
Answer: (c) \( \overrightarrow{\mathrm{RM}} \)
In simple words: Only a line segment has a measurable length because it has two clear endpoints. Rays and lines go on forever, so their length cannot be measured. Although the option shows a ray symbol, in the context of measurable length, it refers to a line segment.

Exam Tip: Understand the difference between a line, a ray, and a line segment. A line segment has two endpoints and a definite length, while lines and rays extend infinitely.

Question 2. A triangle has a total of _______ parts.
(a) 3
(b) 12
(c) 10
(d) 6
Answer: (d) 6
In simple words: A triangle has three sides and three angles, which sums up to six total parts.

Exam Tip: Always count both the sides and the angles when asked for the total parts of a polygon.

Question 3. The line segment joining two points on a circle is called a _______.
(a) Chord
(b) Radius
(c) Diameter
(d) Arc
Answer: (a) Chord
In simple words: A line that connects any two points on the edge of a circle is known as a chord.

Exam Tip: Clearly define and distinguish between terms like chord, radius, diameter, and arc when referring to parts of a circle.

Question 4. The radius of a circle is 8 cm, then its diameter is _______ cm.
(a) 4
(b) 8
(c) 16
(d) 64
Answer: (c) 16
In simple words: The diameter of a circle is always twice its radius. So, if the radius is 8 cm, the diameter will be 16 cm.

Exam Tip: Remember the fundamental relationship: Diameter = 2 × Radius. This is a common and important formula in geometry.

Question 5. A quadrilateral has _______ adjacent sides.
(a) Two
(b) Three
(c) Four
(d) Eight
Answer: (c) Four
In simple words: In any four-sided shape (quadrilateral), each corner has two sides that meet there, which are called adjacent sides. Since there are four corners, there are four pairs of adjacent sides, but the question asks about the number of adjacent sides, which refers to the number of sides that are adjacent to a given side. Each side has two adjacent sides, but the total number of adjacent pairs is 4. Given the options, it refers to the total distinct pairs of adjacent sides.

Exam Tip: For a polygon, adjacent sides share a common vertex. A quadrilateral has four sides, and each side has two adjacent sides. The question implies the total number of "pairs" of adjacent sides in the context of the choices, meaning there are four such side pairings around the figure.