RBSE Solutions Class 6 Maths Chapter 8 Basic Geometrical Concepts and Shapes

(Page No. 112)

Question 1. Mention some places where you notice dots/points in your daily life.
Answer: In our daily life, we see points in many places, such as:
(1) The tip of a light pole near a river.
(2) A lit-up bulb far away at night.
(3) A mark made by a pen on paper.
(4) The tip of a pencil.
(5) A small hole made by a pin. All these examples help us understand what a point is in geometry.
In simple words: We can see dots or points in many everyday things, like a pencil tip or a light bulb far away.

🎯 Exam Tip: When listing everyday examples for geometric concepts, ensure they are distinct and clearly represent the definition.

Question 2. Find out some examples of line segments around you and write their names. Such as corners of wall.....
Answer: Here are some examples of line segments we see every day:
(a) The edges or sides of a table.
(b) A piece of a pencil.
(c) A piece of chalk.
(d) The edges or sides of an almirah (cupboard). Line segments are like straight paths with a clear start and end.
In simple words: Look for straight edges on objects around you, like the side of a table or a piece of chalk; these are line segments.

🎯 Exam Tip: Imagine cutting out a piece of a straight line; if it has a definite beginning and end, it's a line segment.

Question 3. Look at the diagram below A rat is on point A and a piece of chapatti is on point B, Which is the shortest way to reach the chapatti.
Answer: The shortest way for the rat to reach the chapatti from point A to point B will be by going directly from A to B. This is because a straight line connecting two points always shows the shortest distance between them. Any other path would be longer.
In simple words: The shortest way to get from one point to another is always a straight line. So, the rat should go straight from A to B.

🎯 Exam Tip: In geometry, the shortest distance between any two points is always a straight line, a fundamental principle.

(Page No. 116)

Question 1. Kanku says it is more accurate to measure the line by divider than the scale. Do you agree with her? Give a logic to support your answer. (Use Maths kit available in the school).
Answer: Yes, Kanku is correct. A divider measures a line more accurately than a regular scale. This is because a divider uses two sharp tips, allowing for very precise marking of the start and end points of a line without any thickness error from the scale itself. It helps to avoid parallax errors often seen when using a ruler directly.
In simple words: Kanku is right. A divider measures lines better than a ruler because its sharp points can pick up exact start and end positions.

🎯 Exam Tip: Explain that a divider reduces errors like parallax (viewing angle) and measurement starting point inaccuracies, leading to greater precision.

(Page No. 118)

Question 1. Find out some more examples of parallel lines like this in your daily life and write about these.
Answer: Here are some more everyday examples of parallel lines:
(i) The rails of a railway track.
(ii) The edges of a book or notebook.
(iii) The opposite sides of a window frame.
(iv) The opposite edges of a door. Parallel lines are special because they always stay the same distance apart and never cross.
In simple words: Parallel lines are all around us, like the two sides of a book, window, or door, and even railway tracks. They never meet.

🎯 Exam Tip: Remember that parallel lines are defined by never intersecting, no matter how far they extend, and always keeping the same distance apart.

(Page No. 119)

Question 1. 1. If line L ⊥ M then is M ⊥ L? 2. How many line can be perpendicular to any line? 3. Look at the letters of English alphabet L, N, X, Y, T and suggest which of these can be examples of perpendicular lines.
Answer:
1. Yes, if line L is perpendicular to line M (\( L \perp M \)), then line M is also perpendicular to line L (\( M \perp L \)). Perpendicularity is a mutual relationship.
2. An infinite number of lines can be perpendicular to any given line. We can draw countless lines that intersect the given line at a 90-degree angle from different points.
3. From the given letters, L and T are examples of perpendicular lines. In both letters, the two line segments forming them meet at a right angle.
In simple words: If one line is at a right angle to another, then the second line is also at a right angle to the first. You can draw endless lines that are perpendicular to any single line. Letters like L and T show lines meeting at 90 degrees.

🎯 Exam Tip: Perpendicular lines always form right angles (90 degrees) at their intersection, and this relationship works both ways. There are many lines perpendicular to any given line.

Question 1. In the figure, sides .......... Vertex ..........
Answer: In the figure shown, the sides are PQ and PR, and the vertex is P. The vertex is the point where the two sides of an angle meet.
In simple words: In the drawing, the lines that form the shape are PQ and PR. The corner point where they meet is P.

🎯 Exam Tip: Remember that the vertex is always the common point where two line segments or rays meet to form an angle.

(Page No. 126)

Question 1. Now draw angels with the following measurements.
(i) \( \angle ABC = 110^\circ \)
(ii) \( \angle PQR = 40^\circ \)
Answer: The angles are drawn below with the specified measurements:
(i) Angle ABC measuring \( 110^\circ \):

(ii) Angle PQR measuring \( 40^\circ \):

These drawings demonstrate how to construct angles using a protractor, starting from a baseline and measuring the required degrees.
In simple words: The first drawing shows an angle ABC that is 110 degrees wide. The second drawing shows an angle PQR that is 40 degrees wide.

🎯 Exam Tip: Always use a protractor carefully to measure angles. Start from the 0-degree mark on one ray and measure the degrees to the second ray, ensuring the vertex is at the center of the protractor.

(Page No. 137)

Question 1. Look at the diagram and follow the directions of the clock.
(i) Value of an angle from East to South East.
(ii) Value of an angle from East to South West.
(iii) How many right angles are made from East to West?
(iv) After taking three right angle turns from South in which direction we find ourselves?
Answer: Based on the provided diagram and standard clock directions:
(i) The angle from East to South East is \( 45^\circ \). South East is exactly halfway between East and South.
(ii) The angle from East to South West is \( 135^\circ \). This is \( 90^\circ \) (East to South) plus \( 45^\circ \) (South to South West).
(iii) From East to West, we travel \( 180^\circ \). Since one right angle is \( 90^\circ \), \( 180^\circ \) has 2 right angles.
(iv) Starting from South:
1st right turn (clockwise) from South leads to West.
2nd right turn from West leads to North.
3rd right turn from North leads to East. So, after three right angle turns from South, we find ourselves in the East direction. Turning right is moving clockwise.
In simple words: From East to South East is 45 degrees. From East to South West is 135 degrees. Going from East to West makes two 90-degree turns. If you start at South and turn right three times, you will end up facing East.

🎯 Exam Tip: Remember the basic angles between main directions: North, East, South, West are each \( 90^\circ \) apart. Each diagonal direction (like South East) is \( 45^\circ \) from its adjacent main directions.

Text Book Question

(Page No. 110)

Question 1. Some diagrams of different things are given below with their geometrical shapes. Tell us which object shows the shape in its surface.
Answer: Based on the diagrams of different objects and their common geometrical shapes:
1. A brick primarily shows a rectangular shape on its surfaces.
2. An indicator (like a traffic cone) shows a conical or triangular shape from its side view.
3. A torch shows a cylindrical shape.
4. A pettle drum (Damru) shows two conical shapes joined at their vertices.
5. A scale (ruler) shows a rectangular shape or can be considered a line segment. Many everyday items have clear geometric forms.
In simple words: Different things have different shapes. A brick is like a rectangle, a torch is like a cylinder, and a drum is like two cones joined together. A ruler is like a rectangle or a straight line.

🎯 Exam Tip: To identify shapes, focus on the basic outlines of objects. Look for squares, circles, triangles, rectangles, or combinations of these in their visible parts.

(Page No. 111)

Question 1. Mark a point on a paper by pencil. Point (.) is a sign maked by pencil which decides a location.
Answer: To mark a point, simply touch a pencil tip to a paper and make a small dot. This dot (.), which is created by the pencil, acts as a specific sign or mark that precisely defines a location in space. A point has no size, only position.
In simple words: A point is just a tiny dot you make with a pencil. It shows an exact place.

🎯 Exam Tip: Understand that in geometry, a point has no dimension, only a fixed position. It's the most basic element.

(Page No. 114)

Question 1. Look at the above diagram or any scale you have and answer the following.
(1) How many numbers are marked on downside of it?
(2) How many numbers are marked on upside?
(3) How many small marks are there between two consecutive numbers?
Answer: Based on a standard ruler diagram, such as the one provided:
(1) There are 12 numbers marked on the downside of the scale (representing centimeters).
(2) There are 5 numbers marked on the upside of the scale (representing inches).
(3) There are 9 small marks between two consecutive numbers on the centimeter side of the ruler, which divide each centimeter into 10 millimeters. This helps in making very precise measurements.
In simple words: The ruler has 12 numbers on the centimeter side and 5 numbers on the inch side. Between any two main centimeter numbers, there are 9 small marks.

🎯 Exam Tip: When using a ruler, remember that the large numbers mark centimeters (or inches), and the small marks between them indicate millimeters (or fractions of an inch).

Question 2. then 1 mm = ..... cm.
Answer: We know that 10 millimeters (mm) are equal to 1 centimeter (cm).
\( 10 \text{ mm} = 1 \text{ cm} \)
Therefore, to find how many centimeters are in 1 mm, we divide 1 by 10:
\( 1 \text{ mm} = \frac{1}{10} \text{ cm} \)
\( 1 \text{ mm} = 0.1 \text{ cm} \). This conversion is essential for accuracy in measurements.
In simple words: Since 10 millimeters make 1 centimeter, 1 millimeter is the same as 0.1 centimeters.

🎯 Exam Tip: Always remember the conversion: 1 cm = 10 mm. To convert mm to cm, divide by 10; to convert cm to mm, multiply by 10.

Question 3. Ajay and Vijay measured line segment as shown in the diagram. Can you tell us whose answer is right? Should we measure a line segment by putting zero on the scale at the initial point of line?
Answer: In the diagram, both Ajay and Vijay have obtained the correct final measurement for the line segment. However, Ajay's method of starting the measurement from a point other than zero on the scale is not the standard or correct way. The correct way to measure a line segment is always by aligning the zero mark of the scale with the initial point of the line segment. Vijay correctly followed this procedure, which makes his method accurate and standard. Using the zero mark ensures the most direct and error-free measurement.
In simple words: Both Ajay and Vijay got the right answer, but Vijay used the correct method. You should always start measuring a line segment from the zero mark on the ruler.

🎯 Exam Tip: Always start measuring from the zero mark on the ruler to avoid errors and ensure accurate readings.

(Page No. 115)

Question 1. Draw line segments of different lengths and measure them.
Answer: When drawing and measuring line segments, you can create lines of various lengths. Examples of such measured lengths could be:
1. A line segment measuring \( 5 \text{ cm} \).
2. A line segment measuring \( 4 \text{ cm} \).
3. A line segment measuring \( 6 \text{ cm} \).
4. A line segment measuring \( 6.2 \text{ cm} \). Practice helps in drawing lines of exact lengths. These measurements show how different line segments can have different sizes.
In simple words: You can draw straight lines of many different lengths, like 5 cm, 4 cm, 6 cm, or 6.2 cm.

🎯 Exam Tip: Use a ruler and a sharp pencil to draw line segments accurately. Ensure the start and end points are clearly marked at the desired lengths.

Question 1. Whether the following angles are acute, right or obtuse by measuring them with the tester. Also, state their measurements.
Answer: By measuring the angles with a tester and considering their values:
1. Acute angles are angles less than \( 90^\circ \). These include: (i) \( 45^\circ \), (vi) \( 30^\circ \), (vii) \( 45^\circ \).
2. Obtuse angles are angles greater than \( 90^\circ \) but less than \( 180^\circ \). These include: (ii) \( 105^\circ \), (iii) \( 120^\circ \), (v) \( 135^\circ \).
3. Right angles are exactly \( 90^\circ \). This includes: (iv) \( 90^\circ \). Understanding these categories helps classify angles quickly.
In simple words: Angles that are less than 90 degrees are called acute. Angles more than 90 degrees (but less than 180) are obtuse. An angle that is exactly 90 degrees is a right angle.

🎯 Exam Tip: To score full marks, precisely identify if an angle is acute, obtuse, or right-angled, and provide its correct measurement. Remember the definition for each type of angle.