Samacheer Kalvi Class 6 Maths Solutions Term 1 Chapter 4 Geometry Exercise 4.1

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 4 Geometry Ex 4.1

 

Question 1. Fill in the blanks.
(i) A line through two endpoints 'A' and 'B' is denoted by __________.
(ii) A line segment from point 'B' to point 'A' is denoted by __________.
(iii) A ray has __________ endpoint(s).
Answer:
(i) \( \overleftrightarrow{AB} \)
(ii) \( \overline{BA} \)
(iii) one
A line is different from a ray or a line segment because it extends infinitely in both directions, while a ray has one fixed point and a line segment has two fixed endpoints.
In simple words: A line with two points A and B is shown with arrows on both ends. A line segment from B to A is just a bar over BA. A ray always starts from one point and goes on forever in one direction.

🎯 Exam Tip: Remember the notation: a bar for a line segment \( \overline{AB} \), a single arrow for a ray \( \overrightarrow{AB} \), and a double arrow for a line \( \overleftrightarrow{AB} \).

 

Question 2. How many line segments are there in the given line? Name them.

Answer: There are 10 line segments in the given line. A line segment is a part of a line with two distinct endpoints. The line segments are:
\( \overline{PQ} \)
\( \overline{PA} \)
\( \overline{PB} \)
\( \overline{PC} \)
\( \overline{AB} \)
\( \overline{BC} \)
\( \overline{CQ} \)
\( \overline{AQ} \)
\( \overline{BQ} \)
\( \overline{AC} \)
In simple words: We can find 10 different straight pieces, or segments, between any two points on the line. Each pair of points makes one line segment.

🎯 Exam Tip: To count all line segments on a line with 'n' points, use the formula \( \frac{n(n-1)}{2} \). Here, n=5, so \( \frac{5(4)}{2} = 10 \).

 

Question 3. Measure the following line segments.

Answer: We use a ruler to find the lengths of the given line segments. \( \overline{XY} = 2.4 \text{ cm} \)
\( \overline{AB} = 3.4 \text{ cm} \)
\( \overline{EF} = 4 \text{ cm} \)
\( \overline{PQ} = 3 \text{ cm} \)
Each line segment has a fixed length because it is defined by two specific end points.
In simple words: Using a ruler, we find the length of each line piece. XY is 2.4 cm, AB is 3.4 cm, EF is 4 cm, and PQ is 3 cm.

🎯 Exam Tip: Always align the zero mark of the ruler precisely with one endpoint of the line segment to get an accurate measurement.

 

Question 4. Construct a line segment using a ruler and compass.
(1) \( \overline{AB} = 7.5 \text{ cm} \)
(2) \( \overline{CD} = 3.6 \text{ cm} \)
(3) \( \overline{QR} = 10 \text{ cm} \)
Answer:
(1) To construct \( \overline{AB} = 7.5 \text{ cm} \):
(i) Draw a straight line and mark a point 'A' on it.
(ii) Use a compass to measure 7.5 cm. Place the compass pointer at the zero mark of the ruler and extend the pencil tip to 7.5 cm.
(iii) Place the compass pointer on point 'A' on the line and draw a small arc with the pencil. This arc cuts the line at a point; name this point 'B'.
(iv) Now, \( \overline{AB} \) is the required line segment with a length of 7.5 cm.

(2) To construct \( \overline{CD} = 3.6 \text{ cm} \):
(i) Draw a straight line and mark a point 'C' on it.
(ii) Use a compass to measure 3.6 cm. Place the compass pointer at the zero mark of the ruler and extend the pencil tip to 3.6 cm.
(iii) Place the compass pointer on point 'C' on the line and draw a small arc with the pencil. This arc cuts the line at a point; name this point 'D'.
(iv) Now, \( \overline{CD} \) is the required line segment with a length of 3.6 cm.

(3) To construct \( \overline{QR} = 10 \text{ cm} \):
(i) Draw a straight line and mark a point 'Q' on it.
(ii) Use a compass to measure 10 cm. Place the compass pointer at the zero mark of the ruler and extend the pencil tip to 10 cm.
(iii) Place the compass pointer on point 'Q' on the line and draw a small arc with the pencil. This arc cuts the line at a point; name this point 'R'.
(iv) Now, \( \overline{QR} \) is the required line segment with a length of 10 cm.
Constructing line segments accurately is a basic skill in geometry, helping to build more complex shapes.
In simple words: For each length, first draw a line and mark a starting point. Then, open your compass to the correct length using a ruler. Place the compass point on your starting point and draw a small curve on the line to mark the end point. This creates your line segment.

🎯 Exam Tip: Ensure your compass is stable and accurately set to the required measurement on the ruler for precise construction.

 

Question 5. From the given figure
(i) identify the parallel lines
(ii) identify the intersecting lines
(iii) name the points of intersection.

Answer:
(i) Parallel lines are lines that never meet and always stay the same distance apart. The pairs of parallel lines are:
\( \overleftrightarrow{CD} \) and \( \overleftrightarrow{AB} \)
\( \overleftrightarrow{EF} \) and \( \overleftrightarrow{GH} \)
(ii) Intersecting lines are lines that cross each other at a single point. The pairs of intersecting lines are:
\( \overleftrightarrow{CD} \) and \( \overleftrightarrow{EF} \)
\( \overleftrightarrow{CD} \) and \( \overleftrightarrow{GH} \)
\( \overleftrightarrow{AB} \) and \( \overleftrightarrow{EF} \)
\( \overleftrightarrow{AB} \) and \( \overleftrightarrow{GH} \)
(iii) Points of intersection are the exact locations where lines cross. The points of intersection are P, Q, R, and S.
In simple words: Parallel lines run side-by-side without ever touching. Intersecting lines cross each other. The spots where they cross are called points of intersection.

🎯 Exam Tip: Identify parallel lines by looking for lines that maintain a consistent distance, and intersecting lines by observing where they physically cross paths.

 

Question 6. From the given figure, name the
(i) parallel lines
(ii) intersecting lines
(iii) points of intersection.

Answer:
(i) Parallel lines are those that never cross each other, no matter how far they extend. The pairs of parallel lines are:
\( \overleftrightarrow{CD} \) and \( \overleftrightarrow{EF} \)
\( \overleftrightarrow{CD} \) and \( \overleftrightarrow{IJ} \)
\( \overleftrightarrow{EF} \) and \( \overleftrightarrow{IJ} \)
(ii) Intersecting lines are lines that cross at a single point. The pairs of intersecting lines are:
\( \overleftrightarrow{AB} \) and \( \overleftrightarrow{CD} \)
\( \overleftrightarrow{AB} \) and \( \overleftrightarrow{EF} \)
\( \overleftrightarrow{AB} \) and \( \overleftrightarrow{IJ} \)
\( \overleftrightarrow{GH} \) and \( \overleftrightarrow{IJ} \)
\( \overleftrightarrow{AB} \) and \( \overleftrightarrow{GH} \)
(iii) Points of intersection are the specific places where two or more lines meet. The points of intersection are P, Q, and R.
In simple words: Lines that stay apart are parallel. Lines that cross are intersecting. The spots where they cross are called intersection points.

🎯 Exam Tip: When naming lines, you can use any two points on the line, but consistent notation like arrows above letters (e.g., \( \overleftrightarrow{CD} \)) clarifies it's a line, not a segment.

 

Question 7. From the given figure, name
(i) all pairs of parallel lines.
(ii) all pairs of intersecting lines.
(iii) pair of lines whose point of intersection is 'V'.
(iv) point of intersection of the lines 'l2' and 'l5'.
(v) point of intersection of the lines 'l₁' and 'l5'.

Answer:
(i) Parallel lines are those that never intersect. The pairs of parallel lines are:
\( l_3 \) and \( l_4 \)
\( l_4 \) and \( l_5 \)
\( l_3 \) and \( l_5 \)
(ii) Intersecting lines are those that cross each other at some point. The pairs of intersecting lines are:
\( l_1 \) and \( l_2 \)
\( l_1 \) and \( l_3 \)
\( l_1 \) and \( l_4 \)
\( l_1 \) and \( l_5 \)
\( l_2 \) and \( l_3 \)
\( l_2 \) and \( l_4 \)
\( l_2 \) and \( l_5 \)
(iii) The pair of lines whose point of intersection is 'V' are \( l_1 \) and \( l_2 \).
(iv) The point of intersection of the lines 'l2' and 'l5' is 'Q'.
(v) The point of intersection of the lines 'l₁' and 'l5' is 'U'.
Understanding the difference between parallel and intersecting lines helps in describing geometric figures and their relationships.
In simple words: Look for lines that run next to each other without touching (parallel). Look for lines that cross (intersecting). Then, find the exact spot where they cross, which is the point of intersection.

🎯 Exam Tip: Always specify the names of the lines (e.g., \( l_1 \), \( l_2 \)) and the exact letter labels for the points of intersection to ensure clarity and full marks.

 

Question 8. The number of line segments in

(a) 1
(b) 2
(c) 3
(d) 4
Answer: (c) 3
In simple words: Between the three points A, B, and C, there are three possible straight pieces you can make: AB, BC, and AC.

🎯 Exam Tip: For 'n' points on a line, the number of line segments is \( n(n-1)/2 \). Here, for 3 points, it's \( 3(3-1)/2 = 3 \).

 

Question 9. A line is denoted as ___________.
(a) AB
(b) \( \overrightarrow{AB} \)
(c) \( \overleftrightarrow{AB} \)
(d) \( \overline{AB} \)
Answer: (c) \( \overleftrightarrow{AB} \)
In simple words: A line goes on forever in both directions, so it has arrows at both ends in its symbol.

🎯 Exam Tip: Remember that \( \overline{AB} \) denotes a line segment, \( \overrightarrow{AB} \) denotes a ray, and \( \overleftrightarrow{AB} \) denotes a line.