Samacheer Kalvi Class 6 Maths Solutions Term 1 Chapter 4 Geometry Exercise 4.3

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 4 Geometry Ex 4.3

Question 1. Observe the diagram and fill in the blanks.

(i) 'A', 'O' and 'B' are ......... points.
(ii) 'A', 'O' and 'C' are ......... points.
(iii) 'A','B' and 'C'are ......... points.
(iv) ......... is the point of concurrency.
Answer:
(i) 'A', 'O' and 'B' are **collinear** points. These three points lie on the same straight line, forming the diameter of the circle.
(ii) 'A', 'O' and 'C' are **non-collinear** points. These points do not lie on a single straight line, forming a triangle instead.
(iii) 'A','B' and 'C' are **endpoints/non-collinear** points. While A and B are endpoints of a diameter, adding C makes the set of three points non-collinear.
(iv) **O** is the point of concurrency. This is because all diameters and chords passing through the center meet at point O.
In simple words: Collinear points are all in a straight line, like A, O, B. Non-collinear points are not in a straight line, like A, O, C. Point O is where lines meet if they pass through the center of the circle.

🎯 Exam Tip: Remember that "collinear" means "lying on the same line" and "concurrent" means "passing through the same point".

Question 2. Draw any line and mark any 3 points that are collinear.
Answer:

The image shows a straight line 'l' with three points P, Q, and R. Since all three points lie on the same line, they are collinear.
In simple words: Draw a straight line. Put three dots on that line and label them P, Q, and R. These dots are collinear because they are all on the same straight path.

🎯 Exam Tip: Use a ruler to ensure your line is perfectly straight when drawing collinear points.

Question 3. Draw any line and mark any 4 points that are not collinear.
Answer:

The diagram shows three points A, B, and C that lie on a straight line. A fourth point, D, is marked in a different position so it does not lie on the same line as A, B, and C. This way, all four points A, B, C, and D are not collinear when considered together.
In simple words: Draw a line and put three dots (A, B, C) on it. Then, put one more dot (D) somewhere else, not on that line. These four dots together are not in a straight line.

🎯 Exam Tip: To show non-collinear points, ensure at least one point is clearly off the line formed by the others.

Question 4. Draw any 3 lines to have a point of concurrency.
Answer:

The diagram shows three lines \( l_1 \), \( l_2 \), and \( l_3 \) that all pass through the exact same central point. This point where they all meet is called the point of concurrency.
In simple words: Draw three lines so they all cross over at one single point, like spokes on a wheel. That point is where they are concurrent.

🎯 Exam Tip: When drawing concurrent lines, make sure all lines visibly pass through the exact same single point, not just close to it.

Question 5. Draw any 3 lines that are not concurrent. Find the number of points of intersection.
Answer:

The diagram shows three lines, \( l_1 \), \( l_2 \), and \( l_3 \), which do not all pass through the same single point. When three lines are not concurrent, they will typically intersect at three different points, forming a triangle. In this figure, there are **3** points of intersection where each pair of lines crosses.
In simple words: Draw three lines that do not all meet at one place. Each pair of lines will cross, making three separate crossing points in total.

🎯 Exam Tip: If three lines are drawn randomly, they will usually form a triangle and have three intersection points unless they are parallel or concurrent.

Objective Type Questions
Observe the Diagram and give answers

Question 6. A set of collinear points in the figure are
(a) A, B, C
(b) A, F, C
(c) B, C, D
(d) A, C, D
Answer: (b) A, F, C
In simple words: Collinear points are those that lie on the same straight line. In the given figure, points A, F, and C are all on the diagonal line that runs from the bottom-left to the top-right corner.

🎯 Exam Tip: To identify collinear points, mentally trace a straight line through the points. If all points fall on that single line, they are collinear.

Question 7. A set of non-collinear points in the figure are .........
(a) A, F, C
(b) B, F, D
(c) E, F, G
(d)A,D,C
Answer: (d) A, D, C
In simple words: Non-collinear points are points that do not lie on a single straight line. In the diagram, if you try to draw a straight line through A, D, and C, you will find it's not possible; A, D form a side, but C is at another corner, so they create a bent path.

🎯 Exam Tip: For non-collinear points, ensure that even if two points are on a line, the third point is distinctly off that line.

Question 8. A point of concurrency in the figure is
(a) E
(b) F
(c) G
(d) H
Answer: (b) F
In simple words: The point of concurrency is where several lines meet or cross. In the figure, point F is the central point where all the main lines like diagonals and mid-lines intersect.

🎯 Exam Tip: Look for the central point where three or more lines visibly cross each other; this is usually the point of concurrency.