Maharashtra Board Class 6 Maths Chapter 1 Basic Concepts in Geometry Set 1 Solutions

Basic Concepts In Geometry Class 6 Maths Chapter 1 Practice Set 1 Solutions Maharashtra Board

Std 6 Maths Practice Set 1 Solutions Answers

Question 1. Look at the figure alongside and name the following:
ℹ️ चित्र व्याख्या (Diagram Explanation): एक बिंदु O पर प्रतिच्छेद करती हुई कई रेखाएँ और किरणें हैं। चार रेखा खंड (MT, RN, PS) बिंदु O से गुजरते हुए दर्शाए गए हैं, जो विभिन्न दिशाओं में विस्तारित होते हुए किरणें (OP, OM, OR, OS, OT, ON) बनाते हैं। बिंदु P, N, M, T, R, S रेखाओं और किरणों पर स्थित हैं।
(i) Collinear points
(ii) Rays
(iii) Line segments
(iv) Lines
Answer:

🎯 Exam Tip: Accurately identifying and differentiating between collinear points, rays, line segments, and lines from a given figure is crucial for scoring. Pay attention to the arrows (or lack thereof) to distinguish between rays, segments, and lines.

Question 2. Write the different names of the line.
ℹ️ चित्र व्याख्या (Diagram Explanation): एक सीधी रेखा 'l' दर्शाई गई है जिस पर चार बिंदु A, B, C और D क्रम में स्थित हैं।
Answer: The different names of the given line are line l, line AB, line AC, line AD, line BC, line BD and line CD.In simple words: A single line can be named in multiple ways using any two points on it or by its assigned lowercase letter.

🎯 Exam Tip: Remember that a line can be named by any two points lying on it. All combinations of two points on a given line are valid names for that line.

Question 3.
ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र 'ग्रुप ए' और 'ग्रुप बी' के साथ एक मिलान तालिका प्रस्तुत करता है। 'ग्रुप ए' में विभिन्न ज्यामितीय आकृतियों को दर्शाते हुए चार चित्र हैं: (i) दोनों तरफ तीर के निशान वाली एक रेखा, (ii) दो अंत बिंदुओं वाला एक रेखा खंड, (iii) एक सपाट सतह का प्रतिनिधित्व करने वाला एक विमान, और (iv) एक तरफ तीर के निशान वाली एक किरण। 'ग्रुप बी' में 'रे', 'प्लेन', 'लाइन', और 'लाइन सेगमेंट' के लेबल दिए गए हैं।

🎯 Exam Tip: Understanding the visual characteristics of geometric figures-arrows for lines/rays, defined endpoints for segments, and a flat surface for a plane-is essential for accurate identification.

Question 4. Observe the given figure. Name the parallel lines, the concurrent lines and the points of concurrence in the figure.
ℹ️ चित्र व्याख्या (Diagram Explanation): इस आकृति में चार रेखाएँ (a, b, m, p, q) और एक रेखा खंड AD को दर्शाया गया है। रेखाएँ a, b, c, और AD बिंदु A पर प्रतिच्छेद करती हैं। रेखाएँ AD, p, और q बिंदु D पर प्रतिच्छेद करती हैं। रेखाएँ b, m, और q समानांतर प्रतीत होती हैं, और रेखाएँ a, c और p भी समानांतर प्रतीत होती हैं।
Answer:

🎯 Exam Tip: Carefully examine all lines in the figure. For parallel lines, look for lines that maintain a constant distance and never intersect. For concurrent lines, identify sets of lines that all pass through the exact same point.

Maharashtra Board Class 6 Maths Chapter 1 Basic Concepts In Geometry Intext Questions And Activities

Question 1. Complete the rangoli. Then, have a class discussion with the help of the following questions:
1. What kind of surface do you need for making a rangoli?
2. How do you start making a rangoli?
3. What did you do in order to complete the rangoli?
4. Name the different shapes you see in the rangoli.
5. Would it be possible to make a rangoli on a scooter or on an elephant's back?
6. When making a rangoli on paper, what do you use to make the dots?
ℹ️ चित्र व्याख्या (Diagram Explanation): यह एक बिंदीदार ग्रिड पर बनी रंगोली के डिजाइन को दर्शाता है। ग्रिड में क्षैतिज और ऊर्ध्वाधर रूप से समान दूरी पर कई बिंदु हैं, और इन बिंदुओं को जोड़कर विभिन्न ज्यामितीय आकृतियाँ (वर्ग, आयत और त्रिभुज) बनाई गई हैं, जिससे एक सममित पैटर्न बनता है।
Answer:
1. For making a rangoli, I need a flat surface.
2. I can start making a rangoli by drawing equally spaced dots on the flat surface using a chalk.
3. In order to complete the rangoli, I joined the dots by straight lines to make a design.
4. In the rangoli, I find various shapes such as square, rectangle and triangles of two different size.
5. No. It won't be possible to make a rangoli on a scooter or on an elephant's back as they do not have a flat surface.
6. When making a rangoli on paper, I made use of scale and pencil to make equally spaced dots.In simple words: Rangoli making demonstrates geometric concepts by requiring a flat surface, starting with points (dots), connecting them with lines to form shapes, and understanding why certain surfaces are unsuitable for flat designs.

🎯 Exam Tip: This activity reinforces the practical application of basic geometric terms like 'point', 'line', 'surface', and 'shape' in a creative context.

Question 2. Write the proper term, 'intersecting lines' or 'parallel lines' in each of the empty boxes. (Textbook pg. no. 4)
ℹ️ चित्र व्याख्या (Diagram Explanation): यह प्रश्न तीन अलग-अलग आकृतियाँ दिखाता है जिनके साथ खाली बक्से हैं। आकृति (i) में दो रेखाएँ एक-दूसरे को पार करती हुई दिखाई गई हैं। आकृति (ii) में दो रेखाएँ समानांतर और एक-दूसरे से समान दूरी पर दिखाई गई हैं। आकृति (iii) में दो रेखाएँ एक-दूसरे को पार करती हुई दिखाई गई हैं।
(i)
(ii)
(iii)
Answer:
i. Intersecting Lines
ii. Parallel Lines
iii. Intersecting LinesIn simple words: Intersecting lines cross each other at a point, while parallel lines run side-by-side without ever meeting.

🎯 Exam Tip: Distinguishing between intersecting and parallel lines is fundamental. Remember that parallel lines never share a common point, while intersecting lines always cross at one point.

Question 3. Draw a point on the blackboard. Every student now draws a line that passes through that point. How many such lines can be drawn? (Textbook pg. no. 2)
ℹ️ चित्र व्याख्या (Diagram Explanation): एक केंद्रीय बिंदु 'P' है जिससे होकर कई सीधी रेखाएँ विभिन्न दिशाओं में गुजर रही हैं, यह दर्शाता है कि एक ही बिंदु से असीमित रेखाएँ खींची जा सकती हैं।
Answer: An infinite number of lines can be drawn through one point.In simple words: An infinite number of lines can pass through any single point.

🎯 Exam Tip: This concept highlights that a single point does not uniquely define a line; at least two points are needed to define a unique line.

Question 4. Draw a point on a paper and use your ruler to draw lines that pass through it. How many such lines can you draw? (Textbook pg. no. 2)
Answer: An infinite number of lines can be drawn through one point.In simple words: Similar to the blackboard example, countless lines can be drawn through a single point on paper using a ruler.

🎯 Exam Tip: Understand that whether on a blackboard or paper, the geometric principle remains the same: a single point is common to an endless number of lines.

Question 5. There are 9 points in the figure. Name them. (Textbook pg. no. 3)
ℹ️ चित्र व्याख्या (Diagram Explanation): एक आयताकार क्षेत्र में नौ बिंदुओं का एक संग्रह दर्शाया गया है, जो बेतरतीब ढंग से फैला हुआ है।
(i) If you choose any two points, how many lines can pass through the pair?
(ii) Which three or more of these nine points lie on a straight line?
(iii) Of these nine points, name any three or more points which do not lie on the same line.
Answer:
(i) One and only one line can be drawn through two distinct points.
(ii) Points A, B, C and D lie on the same line. Points F, G and C lie on the same line.
ℹ️ चित्र व्याख्या (Diagram Explanation): यह एक ज्यामितीय आकृति है जिसमें विभिन्न बिंदुओं (A, B, C, D, E, F, G, H, I) और रेखाओं को दर्शाया गया है। बिंदु A, B, C, D एक सीधी रेखा पर हैं, और बिंदु F, G, C भी एक सीधी रेखा पर हैं जो पिछली रेखा को प्रतिच्छेद करती है।
(iii) Points E, F, G, H and I do not lie on the same line, points A, B, E, H and I do not lie on the same line.In simple words: This question explores collinearity and non-collinearity; exactly one line connects two points, while three or more points may or may not lie on the same line.

🎯 Exam Tip: For collinearity questions, use a ruler to check if multiple points align. Remember that any two distinct points always define a unique line.

Question 6. Observe the picture of the game being played. Identify the collinear players, non-collinear players, parallel lines and the plane. (Textbook pg. no. 4)
ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र एक दौड़ प्रतियोगिता में भाग ले रहे खिलाड़ियों के समूह को दर्शाता है। खिलाड़ी एक सीधी रेखा में खड़े हैं, दौड़ के ट्रैक के साथ। ट्रैक पर कई समानांतर रेखाएँ खींची गई हैं, जो दौड़ की लेन को परिभाषित करती हैं।
Answer:

🎯 Exam Tip: Real-world examples like a running track are excellent for visualizing geometric concepts. Collinear objects lie on a straight line, parallel lines never meet, and a flat surface represents a plane.

Question 7. In January, we can see the constellation of Orion in the eastern sky after seven in the evening. Then it moves up slowly in the sky. Can you see the three collinear stars in this constellation? Do you also see a bright star on the same line some distance away? (Textbook pg. no. 4)
ℹ️ चित्र व्याख्या (Diagram Explanation): यह एक खगोलीय दृश्य को दर्शाता है जहाँ कई तारे अंतरिक्ष में बिखरे हुए हैं, जिनमें कुछ तारे एक सीधी रेखा में संरेखित हैं और कुछ नहीं।
Answer:
1. The three stars shown by points C, D and E are collinear.
2. The star shown by point H lies on the same line as the stars C, D and E.
ℹ️ चित्र व्याख्या (Diagram Explanation): यह एक तारे के पैटर्न को दर्शाता है जिसमें बिंदु C, D, E एक सीधी रेखा में हैं, और बिंदु H भी उसी रेखा पर स्थित है लेकिन कुछ दूरी पर है। अन्य बिंदु A, B, F, G इस रेखा से बाहर हैं।In simple words: This question relates the geometric concept of collinearity to stars in a constellation, showing how certain stars appear to align on a single line.

🎯 Exam Tip: Observing natural phenomena like star constellations can help solidify the abstract concept of collinearity. Look for any three or more points (stars) that appear to fall on a single straight line.

Question 8. Maths is fun! (Textbook pg. no. 5) Take a flat piece of thermocol or cardboard, a needle and thread. Tie a big knot or button or bead at one end of the thread. Thread the needle with the other end. Pass the needle up through any convenient point P. Pull the thread up, leaving the knot or the button below. Remove the needle and put it aside. Now hold the free end of the thread and gently pull it straight. Which figure do you see? Now, holding the thread straight, turn it in different directions. See how a countless number of lines can pass through a single point P.
ℹ️ चित्र व्याख्या (Diagram Explanation): यह एक हाथ को दर्शाता है जो एक बिंदु 'P' के माध्यम से एक धागे को खींच रहा है, जिससे धागा एक सीधी रेखा का प्रतिनिधित्व करता है।
Answer:
1. The pulled thread forms a straight line.
2. An infinite number of lines can be drawn through one point.In simple words: This activity demonstrates that a taut thread represents a straight line and that an infinite number of straight lines can pass through a single point.

🎯 Exam Tip: Hands-on activities are excellent for understanding fundamental geometric principles. This experiment clearly illustrates the concept of a line and the property of multiple lines passing through a single point.

Question 9. Choose the correct option for each of the following questions:
(i) ______ is used to name a point.
(A) Capital letter
(B) Small letter
(C) Number
(D) Roman numeral
Answer: (A) Capital letterIn simple words: Points in geometry are conventionally named using capital letters.

🎯 Exam Tip: Remember standard geometric notation: points are named with capital letters, lines with lowercase letters, and planes often with a single capital script letter or three non-collinear points.

Question 9.
(ii) A line segment has two points showing its limits. They are called_______
(A) origin
(B) end points
(C) arrow heads
(D) infinite points
Answer: (B) end pointsIn simple words: A line segment is defined by its two distinct end points, which mark its beginning and end.

🎯 Exam Tip: Understand that line segments are finite in length, unlike lines or rays, because they have clearly defined end points.

Question 9.
(iii) An arrow head is drawn at one end of the ray to show that it is ______ on that side.
(A) finite
(B) ending
(C) infinite
(D) broken
Answer: (C) infiniteIn simple words: The arrow on a ray signifies that it extends without limit in that specific direction.

🎯 Exam Tip: The arrow is a key visual cue for rays and lines, indicating endless extension, whereas line segments have no arrows.

Question 9.
(iv) Lines which lie in the same plane but do not intersect are said to be ______ to each other.
(A) intersecting
(B) collinear
(C) parallel
(D) non-collinear
Answer: (C) parallelIn simple words: Lines on the same flat surface that never cross each other are called parallel lines.

🎯 Exam Tip: The definition of parallel lines includes two critical conditions: they must be in the same plane, and they must never intersect.

Question 10. Determine the collinear and non-collinear points in the figure alongside:
ℹ️ चित्र व्याख्या (Diagram Explanation): यह एक ज्यामितीय आकृति है जिसमें विभिन्न बिंदु (A, B, C, D, E, F, G, H, I) और रेखाएँ दर्शाई गई हैं। कुछ बिंदु एक सीधी रेखा पर हैं (जैसे A, E, H, C और B, E, I, D), जबकि अन्य बिंदु एक ही रेखा पर नहीं हैं।
Answer:
Collinear points:
1. Points A, E, H and C.
2. Points B, E, I and D.
Non-collinear points:
Points B, G, F and IIn simple words: Collinear points lie on a single straight line, whereas non-collinear points do not share a common straight line.

🎯 Exam Tip: When identifying collinear points, visually extend lines through points to confirm if three or more align. For non-collinear points, ensure no single straight line can pass through all of them simultaneously.

Question 11. Look at the figure alongside and answer the questions given below:
(i) Name the parallel lines.
(ii) Name the concurrent lines and the point of concurrence.
(iii) Write the different names of line PV.
ℹ️ चित्र व्याख्या (Diagram Explanation): यह एक ज्यामितीय आकृति है जिसमें कई रेखाएँ (l, m, n, p, q, r, s) और बिंदु (P, Q, R, S, T, U, V, W) दर्शाए गए हैं। रेखाएँ p, q, r, s समानांतर दिखाई देती हैं, और रेखाएँ l, m, n भी समानांतर प्रतीत होती हैं। रेखा q, l, m, n बिंदु S पर प्रतिच्छेद करती हैं।
Answer:
i. Parallel lines:
a. line l and line n
b. line p, line q, line r and line s
ii. Concurrent Lines: line q, line m, line n
Point of Concurrence: point S
iii. line l, line PT, line PR, line PV, line RT, line RV and line TV.In simple words: This question requires identifying lines that never meet (parallel), lines that cross at one point (concurrent), and all possible names for a specific line using its points.

🎯 Exam Tip: For complex figures, systematically identify lines, then check for parallelism (no intersection) and concurrence (multiple lines through a single point). For naming lines, any two points on the line are sufficient.

Question 12. Name the different line segments and rays in the given figure:
ℹ️ चित्र व्याख्या (Diagram Explanation): यह आकृति एक बिंदु 'O' को दर्शाती है जिससे दो किरणें (OX और OY) ऊपर की ओर और दो किरणें (OV और OU) नीचे की ओर अलग-अलग दिशाओं में निकल रही हैं। बिंदु X, Y, V, U इन किरणों पर स्थित हैं।
Answer:
Line Segments:
seg UV, seg OY, seg OX, seg OV and seg OU
Rays:
ray OV, ray OX, ray OY and ray UV.In simple words: Identify all parts of the figure that have two definite endpoints (line segments) and all parts that start at one point and extend infinitely in one direction (rays).

🎯 Exam Tip: Pay close attention to endpoints and arrows. A segment has two endpoints, a ray has one endpoint and one arrow, and a line has two arrows, each indicating infinite extension.