Exercise 4.1 - Chapter 4 Geometry Term 1 6th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Ex $4.1$
Question $1 .$
Fill in the blanks.
(i) A line through two endpoints ' $A$ ' and ' $B$ ' is denoted by
(ii) Aline segment from point ' $\mathrm{B}$ ' to point ' $\mathrm{A}$ ' is denoted by
(iii) A ray has endpoint(s).
Solution:
(i) $\overleftrightarrow{A B}$
(ii) $\overline{B A}$
(iii) one

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

Solution:
(i) There are 10 line segments.
(ii) They are $\overline{\mathrm{PA}}, \overline{\mathrm{AB}}, \overline{\mathrm{BC}}, \overline{\mathrm{CQ}}, \overline{\mathrm{PB}}, \overline{\mathrm{AC}}, \overline{\mathrm{BQ}}, \overline{\mathrm{PC}}, \overline{\mathrm{AQ}}$ and $\overline{\mathrm{PQ}}$
 

Question $3 .$
Measure the following line segments.

Solution:
$\overline{\mathrm{XY}}=2.4 \mathrm{~cm} ; \overline{\mathrm{AB}}=3.4 \mathrm{~cm} ; \overline{\mathrm{EF}}=4 \mathrm{~cm} ; \overline{\mathrm{PQ}}=3 \mathrm{~cm}$

Question $4 .$
Construct a line segment using ruler and compass.
(i) $\overline{\mathrm{AB}}=7.5 \mathrm{~cm}$
(ii) $\overline{\mathrm{CD}}=3.6 \mathrm{~cm}$
(iii) $\overline{\mathrm{QR}}=10 \mathrm{~cm}$
Solution:
(i) $\overline{\mathrm{AB}}=7.5 \mathrm{~cm}$
A $1.5 \mathrm{~cm} \quad$ B $l$
Construction:

Step 1: Drawn a line 1 and marked point $\mathrm{A}$.
Step 2: Measured $7.5 \mathrm{~cm}$ using compass placing the pointer at ' 0 ' and pencil pointer at $7.5 \mathrm{~cm}$. Step 3: Placing a compass pointer at A, drawn an arc on 1 with the pencil pointer. It cut 1 at B. Step 4: $\mathrm{AB}$ is the required segment of length $7.5 \mathrm{~cm}$.
(ii) $\overline{\mathrm{CD}}=3.6 \mathrm{~cm}$
Construction:

Step 1: Drawn a line $l$ and marked the point ' ${ }^{\prime}$ ' on it.
Step 2: Measured $3.6 \mathrm{~cm}$ using a compass by placing the pointer at ' $\mathrm{O}$ ' and pencil at $3.6 \mathrm{~cm}$ Step 3: Placing pointer at $\mathrm{C}$ drawn the arc on 'l' with pencil pointer
Step 4: CD is the required line segment of length $3.6 \mathrm{~cm}$

(iii) $\overline{\mathrm{QR}}=10 \mathrm{~cm}$

Construction:
Step 1: Drawn a line 'l' and marked the point $Q$ on it
Step 2: Measured $10 \mathrm{~cm}$ using a compass by placing the pointer at ' 0 ' and pencil pointer at $10 \mathrm{~cm}$.
Step 3: Placing pointer at Q drawn the arc on 'l' with pencil pointer and named the point $R$
Step 4: QR is the required line segments of $10 \mathrm{~cm}$.

Question 5 .
From the given figure

(i) identify the parallel lines
(ii) identify the intersecting lines
(iii) name the points of intersection
Solution:
(i) Parallel lines:
(a) $\overrightarrow{\mathrm{CD}}$ and $\overrightarrow{\mathrm{AB}}$
(b) $\overrightarrow{\mathrm{EF}}$ and $\overrightarrow{\mathrm{GH}}$
(ii) Intersecting lines:
(a) $\overrightarrow{\mathrm{CD}}$ and $\overrightarrow{\mathrm{EF}}$
(b) $\overrightarrow{\mathrm{CD}}$ and $\overrightarrow{\mathrm{GH}}$
(c) $\overrightarrow{\mathrm{AB}}$ and $\overrightarrow{\mathrm{EF}}$
(d) $\overrightarrow{\mathrm{AB}}$ and $\overrightarrow{\mathrm{GH}}$
(iii) Point of Intersection:$\mathrm{P}, \mathrm{Q}, \mathrm{R}$ and $\mathrm{S}$ are the points of Intersection.

Question 6.

From the given figure, name the (i) parallel lines (ii) intersecting lines (iii) points of Intersection

Solution:
(i) Parallel lines:
$\overrightarrow{\mathrm{CD}}$ and $\overrightarrow{\mathrm{EF}} ; \overrightarrow{\mathrm{CD}}$ and $\overrightarrow{\mathrm{IJ}} ; \overrightarrow{\mathrm{EF}}$ and $\overrightarrow{\mathrm{IJ}}$ are parallel lines.
(ii) Intersecting lines:
(a) $\overrightarrow{\mathrm{AB}}$ and $\overrightarrow{\mathrm{CD}}$
(b) $\overrightarrow{\mathrm{AB}}$ and $\overrightarrow{\mathrm{EF}}$
(c) $\overrightarrow{\mathrm{AB}}$ and $\overrightarrow{\mathrm{GH}}$
(d) $\overrightarrow{\mathrm{AB}}$ and $\overrightarrow{\mathrm{IJ}}$
(e) $\overrightarrow{\mathrm{GH}}$ and $\overrightarrow{\mathrm{IJ}}$
Points of Intersection:
$P, Q$ and $R$ are the points of intersection.
 

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 ' $\mathrm{V}$ '
(iv) point of intersection of the lines ' $\mathrm{l}_{2}$ ' and ' $\mathrm{l}_{3}$ '
(v) point of intersection of the lines ' $l_{1}$ ' and 'l $_{5}$ "

Solution:
(i) Pairs of parallel lines:
- $\mathrm{l}_{3}$ and $\mathrm{l}_{4}$
- $\mathrm{l}_{4}$ and $\mathrm{l}_{5}$
- $\mathrm{l}_{3}$ and $\mathrm{l}_{5}$
(ii) Pairs of intersecting lines:
- $\mathrm{l}_{1}$ and $\mathrm{l}_{2}$
- $\mathrm{l}_{1}$ and $\mathrm{l}_{3}$
- $\mathrm{l}_{1}$ and $\mathrm{l}_{4}$
- $\mathrm{l}_{1}$ and $\mathrm{l}_{5}$
- $\mathrm{l}_{2}$ and $\mathrm{l}_{3}$
- $\mathrm{l}_{2}$ and $\mathrm{l}_{4}$
- $\mathrm{l}_{2}$ and $\mathrm{l}_{5}$
(iii) $\mathrm{l}_{1}$ and $\mathrm{l}_{2}$ intersect at ' $\mathrm{V}$ '
(iv) point of intersection of the lines ' $l_{2}$ ' and; $1_{5}$ ' is ' $Q$ '
(v) point of intersection of the lines ' $\mathrm{l}_{1}$ ' and ' $\mathrm{l}_{5}$ ' is ' $\mathrm{U}$ '

Objective Type Questions
Question 8 .
The number of line segments in

(a) 1
(b) 2
(c) 3
(d) 4
Solution:
(c) 3
Hint: $\overline{\mathrm{AB}}, \overline{\mathrm{AC}}, \overline{\mathrm{BC}}$
 

Question 9 .
A line is denoted as
(a) $\mathrm{AB}$

(b) $\overrightarrow{A B}$
(c) $\overleftrightarrow{A B}$
(d) $\overline{A B}$
Solution:
(c) $\overleftrightarrow{A B}$