In Text Questions Try These (Text Book No. 90, 91, 93, 94, 98, 99) - Chapter 5 Geometry Term 1 7th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Try this (Text book Page No. 90)
Question $1 .$
What would happen to the angles if we add 3 or 4 or 5 rays on a line as given below?

Solution:
New adjacent angles are formed.
The new angles become smaller in measure. But their sum is $180^{\circ}$ as it is a linear angle.

Try this (Text book Page No. 90 )
Question $1 .$
Can you justify the statement

$\angle \mathrm{AOB}+\angle \mathrm{BOC}+\angle \mathrm{COD}+\angle \mathrm{DOE}+\angle \mathrm{EOF}+\angle \mathrm{FOA}=360^{\circ} \text { ? }$
Solution:
We know that the sum of angles at a point is $360^{\circ}$
$\angle \mathrm{AOB}+\angle \mathrm{BOC}+\angle \mathrm{COD}+\angle \mathrm{DOE}+\angle \mathrm{EOF}+\angle \mathrm{FOA}=360^{\circ}$ as they are the sum of angles at the point ' $\mathrm{O}$ '

Try These (Text book Page No. 91)
Question $1 .$
Four real life examples of vertically opposite angles are given below.

Solution:
(i) The four angles made in the scissors where the opposite angles are always equal.
(ii) The point where two roads intersect each other.
(iii) Rail road crossing signs.
(iv) An hourglass.

Question $2 .$
In the given figure two lines $\overleftrightarrow{A B}$ and $\overleftrightarrow{C D}$ intersect at ' $\mathrm{O}$ '. Observe the pair of angles and complete the following table. One is done for you.

Question $3 .$
Name the two pairs of vertically opposite angles

$\angle \mathrm{PTS}$ and $\angle \mathrm{QTR}$ are vertically opposite angles. $\angle \mathrm{PTR}$ and $\angle \mathrm{QTS}$ are vertically opposite angles.
 

Question $4 .$
Find the value of $x^{\circ}$ in the figure given below.

Solution:
Lines 1 and $m$ intersect at a point and making a pair of vertically opposite angles $x^{\circ}$ and $150^{\circ}$.
We know that vertically opposite angles are equal.
$\mathrm{x}=150^{\circ}$
 

Exercise 5.2
Try this (Text book Page No. 93)
Question 1 .
For a given set of lines, it is possible to draw more than one transversal.

Solution:
Yes, it is possible to draw more than one transversal for a given set of lines. 1 and $\mathrm{m}$ are given set of lines. $\mathrm{n}$ and $\mathrm{p}$ are transversal

Try these (Text Book Page No 94)
Question $1 .$
Draw as many possible transversals in the given figures.

(i) $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are transversal to $\mathrm{l}, \mathrm{m}$ and $\mathrm{n}$.
(ii) $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are transversal to $\mathrm{l}, \mathrm{m}, \mathrm{n}$ and $\mathrm{p}$. More transversals can be drawn.

Question $2 .$
Draw a line which is not the transversal to the above figures.
Solution:

Question $3 .$
How many transversals can you draw for the following two lines

Infinite number of transversals can be drawn.
$\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}, \mathrm{e}, \mathrm{f}, \mathrm{g}$ are transversal to $\mathrm{m}$ and $\mathrm{n}$.

Try these (Text book Page No. 96)
Question $1 .$
Four real life examples for transversal of parallel lines are given below.

Give four more examples for transversal of parallel lines seen in your surroundings.
Solution:
Some examples of parallel lines in our surroundings
(i) Zebra crossing on the road.
(ii) Railway tracks with sleepers.

(iii) Steps
(iv) Parallel bars in men's gymnastics

Question $2 .$
Find the value of $\mathrm{x}$.

Solution:
(i) We know that if two parallel lines are cut by a transversal, each pair of corresponding angles are equal. $\therefore \mathrm{x}=125^{\circ}$
(ii) $\mathrm{m}$ and $\mathrm{n}$ are parallel lines and $\mathrm{l}$ is a transversal $\mathrm{x}^{\circ}$ and $48^{\circ}$ are corresponding angles. $\therefore \mathrm{x}=48^{\circ}$
(iii) $\mathrm{m}$ and $\mathrm{n}$ are parallel lines and 7 ' is the transversal.
$\therefore$ Corresponding angles are equal.
$\therefore \mathrm{x}^{\circ}=138^{\circ}$

Try these (Text book Page No. 98)
Question $1 .$
Find the value of $x^{\circ}$.

(i) $\mathrm{m}$ and $\mathrm{n}$ are parallel lines. ' $\mathrm{l}$ ' is a transversal.
When two parallel lines are cut by a transversal each pair of alternate interior angles are equal. $\therefore \mathrm{x}^{\circ}=127^{\circ}$
(ii) $\mathrm{m}$ and $\mathrm{n}$ are parallel lines and 1 is the transversal.
When two parallel lines are cut by a transversal each pair of alternate exterior angles are equal. $\therefore \mathrm{x}^{\circ}=46^{\circ}$
 

Try These (Text Book Page No. 99)
Question $1 .$
Find the values of $\mathrm{x}$.

Solution:
(i) $\mathrm{m}$ and $\mathrm{n}$ are parallel lines and $\mathrm{l}$ is the transversal.
When two parallel lines are cut by a transversal, each pair of interior angles that lie on the same side of the transversal are supplementary
$\begin{aligned}
\therefore x^{\circ}+33^{\circ} &=180^{\circ} \\
x^{\circ} &=180^{\circ}-33^{\circ} \\
&=147^{\circ} \\
\therefore x &=147^{\circ}
\end{aligned}$
(ii) $\mathrm{m}$ and $\mathrm{n}$ are parallel line and $\mathrm{l}$ is the transversal.
When two parallel lines are cut by a transversal, each pair of exterior angles that lie on the same side of the transversal are supplementary.
the same side of the transversal are supplementary.
$\begin{aligned}
&\therefore \mathrm{x}^{\circ}+132^{\circ}=180^{\circ} \\
&\mathrm{x}^{\circ}=180^{\circ}-132^{\circ} \\
&=48^{\circ} \\
&\therefore \mathrm{x}=48^{\circ}
\end{aligned}$
 

Exercise $5.3$
Question $1 .$
What will happen If the radius of the arc is less than half of $\mathrm{AB}$ ?

Solution:
If the radius of the arc is less than half of $\mathrm{AB}$, then both the arcs will not cut at a point and we can't draw perpendicular bisector.