Lines and Angle Important questions

Section 1

Question 1
Use the figure to name:
(a) Five points
(b) A line
(c) Four rays
(d) Five-line segments

Solution

Point	A point determines a location. It is usually denoted by a capital letter
Line segment	A line segment corresponds to the shortest distance between two points. The line segment joining points X and X is denoted by XY.
Line	A line segment extended on both side to indefinitely is called line
Ray	A ray is a portion of line starting at a point and going in one direction endlessly.

(a) D, E, O,B,C
(b) $\overleftrightarrow {BD}$
(c) $\overrightarrow{OD}$,$ \overrightarrow{OC}$, $ \overrightarrow{OB}$, $ \overrightarrow{ED}$
(d) $\overline{OE}$,$\overline{BE}$,$\overline{OD}$,$\overline{OB}$,$\overline{OC}$

Question 2
Name the line given in all possible (twelve) ways, choosing only two letters at a time from the four given

Solution
$\overleftrightarrow {AB}$, $\overleftrightarrow {BC}$,$\overleftrightarrow {CD}$,$\overleftrightarrow {AD}$,$\overleftrightarrow {BD}$,$\overleftrightarrow {AC}$,$\overleftrightarrow {BA}$, $\overleftrightarrow {CB}$,$\overleftrightarrow {DC}$,$\overleftrightarrow {DB}$,$\overleftrightarrow {CA}$,$\overleftrightarrow {DA}$

Question 3
Use the figure to name:
(a) Line containing point E.
(b) Line passing through A.
(c) Line on which O lies
(d) Two pairs of intersecting lines.

Solution
a)$\overleftrightarrow {FE}$
b) $\overleftrightarrow {AE}$
c) $\overleftrightarrow {OC}$
d) $\overleftrightarrow {AD}$ & $\overleftrightarrow {OC}$
$\overleftrightarrow {AE}$ & $\overleftrightarrow {OF}$
 
Question 4
How many lines can pass through (a) one given point? (b) two given points?
Solution
(i) There are infinite lines which can pass through one point.
(ii) There is only one line which can pass through two given points.
 
Question 5
Draw a rough figure and label suitably in each of the following cases:
(a) Point P lies on $\overline{AB}$
(b) $\overleftrightarrow {XY}$ and $\overleftrightarrow {PQ}$ intersect at M.
(c) Line l contains E and F but not D.
(d) $\overleftrightarrow {OP}$ and $\overleftrightarrow {OQ}$ meet at O.
 
Solution
a)

b)

c)

d)

 
Question 6
Consider the following figure of line $\overleftrightarrow {MN}$
Say whether following statements are true or false in context of the given figure.
(a) Q, M, O, N, P are points on the line $\overleftrightarrow {MN}$.
(b) M, O, N are points on a line segment $\overline{MN}$ .
(c) M and N are end points of line segment $\overline{MN}$ .
(d) O and N are end points of line segment $\overline{OP}$ .
(e) M is one of the end points of line segment $\overline{QO}$ .
(f) M is point on ray $\overrightarrow{OP}$
(g) Ray $\overrightarrow{OP}$ is different from ray $\overrightarrow{QP}$
(h) Ray $\overrightarrow{OP}$  is same as ray $\overrightarrow{OM}$
(i) Ray $\overrightarrow{OM}$  is not opposite to ray $\overrightarrow{OP}$
(j) O is not an initial point of $\overrightarrow{OP}$
(k) N is the initial point of $\overrightarrow{NP}$  and $\overrightarrow{NM}$.

Solution
(a) True
(b) True
(c) True
(d) False
(e) False
(f) False
(g) True
(h) False
(i) False
(j) False
(k) True

Section 2

Question 1
Name the angles in the given figure.

Solution
$ \angle DAB $, $ \angle CBA $ , $ \angle ADC $, $ \angle DCB $
 
Question 2
In the given diagram, name the point(s)
(a) In the interior of $ \angle DOE $
(b) In the exterior of $ \angle EOF $
(c) On $ \angle EOF $

Solution
(a) Point interior of $ \angle DOE $ : A
(b) Points exterior of $ \angle EOF $: C, A, D
(c) Points on $ \angle EOF $: E, O, B, F
Question 3
Draw rough diagrams of two angles such that they have
(a) One point in common.
(b) Two points in common.
(c) Three points in common.
(d) Four points in common.
(e) One ray in common.
Solution
a)

O is the common point for two angles $ \angle AOB $ and $ \angle DOC $
 
b)

O and B are  the common point for two angles  $ \angle AOB $  and  $ \angle BOC $
 
c)

 O  , E and B are  the common point for two angles  $ \angle AOB $ and  $ \angle  BOC $
d)

O, B, C and D are common points for two angles  $ \angle  XOD   $ and  $ \angle YOD $
e)

OX is the ray common between the angle   $ \angle BOX $  and  $ \angle AOX $
 
Question 1
What is the disadvantage in comparing line segments by mere observation?
Answer
You may be correct when the difference is obvious
But comparison become difficult when the difference in lengths between these two may not be obvious.
 
Question 2
Why is it better to use a divider than a ruler, while measuring the length of a line segment?
Answer
Ruler can be error prone because of two reasons
(a) thickness of the ruler
(b) Incorrect positioning of the eye will give wrong measurement
So, it is better to use divider than a ruler
 
Question 3.
Draw any line segment, say AB. Take any point C lying in between A and B.
Measure the lengths of AB, BC and AC. Is AB = AC + CB?
[Note: If A, B, C are any three points on a line such that AC + CB = AB, then we can be sure that C lies between A and B.]
Answer
Draw the line and then measure each line segment to check it
 
Question 4.
If A, B, C are three points on a line such that AB = 5 cm, BC = 3 cm and AC = 8 cm, which one of them lies between the other two?
Answer
Given that,
AB =5 cm
BC = 3 cm
AC = 8 cm
Here, AC = AB + BC
Therefore, point B is lying between A and C.
 
 
Question 5.
Verify, whether D is the midpoint of AG.

Answer
We have
AD= 3 units
DG= 3 units
AG =6 units
So, D is the midpoint of AG
 
Question 6.
 If B is the mid-point of AC and C is the mid-point of BD, where A, B, C, D lie on a straight line, say why AB = CD?
Answer

AB =BC (as B is mid-point)
BC=CD (as C is the mid-point)
Therefore
AB=CD
 
Question 7.
Draw five triangles and measure their sides. Check in each case, if the sum of the lengths of any two sides is always less than the third side.
 

Section 3

Question 1
What fraction of a clockwise revolution does the hour hand of a clock turn through, when it goes from
(a) 3 to 9
(b) 4 to 7
(c) 7 to 10
(d) 12 to 9
(e) 1 to 10
(f) 6 to 3
 
Answer
(a) 1/2 or two right angles.
(b) 1/4 or one right angle.
(c) 1/4 or one right angle.
(d) 3/4 or three right angles.
(e) 3/4 or three right angles.
(f) 3/4 or three right angles.
 
Question 2. Where will the hand of a clock stop if it?
(a) starts at 12 and makes ½ of a revolution, clockwise?
(b) starts at 2 and makes ½ of a revolution, clockwise?
(c) starts at 5 and makes ¼ of a revolution, clockwise?
(d) starts at 5 and makes ¾ of a revolution, clockwise?
Answer
(a) At 6
(b) At 8
(c) At 8
(d) At 2
 
Question 3
Which direction will you face if you start facing
(a) east and make ½ of a revolution clockwise?
(b) east and make $1 \frac {1}{2}$ of a revolution clockwise?
(c) west and make ¾ of a revolution anti-clockwise?
(d) south and make one full revolution?
(Should we specify clockwise or anti-clockwise for this last question? Why not?)
Answer
a) west
b) west
c) North
d) south
 
Question 4
What part of a revolution have you turned through if you stand facing
(a) east and turn clockwise to face north?
(b) south and turn clockwise to face east?
(c) west and turn clockwise to face east?
Answer
a) ¾
b) ¾
c) ½
 
Question 5.
Find the number of right angles turned through by the hour hand of a clock when it goes from
(a) 3 to 6
(b) 2 to 8
(c) 5 to 11
(d) 10 to 1
(e) 12 to 9
(f) 12 to 6
Answer
(a) One right angle
(b) Two right angles
(c) Two right angles
(d) One right angle
(e) Three right angles
(f) Two right angles
 
Question 6.
How many right angles do you make if you start facing
(a) south and turn clockwise to west?
(b) north and turn anti-clockwise to east?
(c) west and turn to west?
(d) south and turn to north?
Answer
(a) One right angle
(b) Three right angles
(c) Four right angles
(d) Two right angles
 
Question 7
Where will the hour hand of a clock stop if it starts
(a) from 6 and turns through 1 right angle?
(b) from 8 and turns through 2 right angles?
(c) from 10 and turns through 3 right angles?
(d) from 7 and turns through 2 straight angles?
Answer
(a) At 9
(b) At 2
(c) At 7
(d) At 7
 

section 4

Question 1
Match the correct options

(A) Straight angle	(i) Less than one-fourth of a revolution
(B) Right angle	(ii) More than half a revolution
(C) Acute angle	(iii) Half of a revolution
(D) Obtuse angle	(iv) One-fourth of a revolution
(E) Reflex angle	(v) Between 14 and 12 of a revolution
	(vi) One complete revolution

 
Answer
(A) Straight angle — iii) Half of a revolution
As $180^0$ is considered as a straight line and half of revolution is also $180^0$
(B) Right angle — iv) One-fourth of a revolution
As Right angle and One-fourth of a revolution are both $90^0$
(C) Acute angle — i) Less than one-fourth of a revolution
As The angle which is less than 90 is called acute angle and less than one-fourth of a revolution is the angle less than $90^0$
(D) Obtuse angle — v) Between 14 and 12 of a revolution
Obtuse angle   is the angle which is greater than 90 and less than 180 and the value between 14 and 12 of a revolution also lies between 90 and 180
(E) Reflex angle – ii) More than half a revolution
Reflex angle is the angle which is greater than $180^0$ but less than $360^0$ and more than half a revolution is the angle whose measure is greater than $180^0$
 
Question 2
Classify each one of the following angles as right, straight, acute, obtuse or reflex:

Answer
(a) Acute
(b) obtuse
(c) Right angle
(d) reflex angle
(e) straight angle
(f) Acute
 

Section 5

 
Question 1.
What is the measure of
(i) a right angle?
(ii) a straight angle?
Answer
(a) $90^0$
(b) $180^0$
 
Question 2.
Say True or False:
(a) The measure of an acute angle < 90°.
(b) The measure of an obtuse angle < 90°.
(c) The measure of a reflex angle > 180°.
(d) The measure of one complete revolution = 360°.
(e) If m∠ÐA = 53° and m∠ÐB = 35°, then m∠ÐA > Ðm∠B.
Answer
(a) true
(b) false
(c) true
(d) true
(e) True
 
Question 3.
Write down the measures of
(a) some acute angles.
(b) some obtuse angles.
(give at least two examples of each).
Answer
(i) Acute angles
$60^0$
$45^0$
(ii) Obtuse angles
$120^0$
$160^0$
Question 4.
Measure the angles given below using the Protractor and write down the measure

Answer
a) $40^0$
b) $130^0$
c) $90^0$
d) $60^0$
 
Question 5
Which angle has a large measure?

First estimate and then measure.
Measure of Angle A =
Measure of Angle B =
Answer
A measure $40^0$
B measures $60^0$
∠A has the largest angle.
 
Question 6
From these two angles which has larger measure? Estimate and then confirm by measuring them.

Answer
The angles are $70^0$ and $75^0$
 
Question 7
Fill in the blanks with acute, obtuse, right or straight:
(a) An angle whose measure is less than that of a right angle is______.
(b) An angle whose measure is greater than that of a right angle is ______.
(c) An angle whose measure is the sum of the measures of two right angles is _____.
(d) When the sum of the measures of two angles is that of a right angle, then each one of them is ______.
(e) When the sum of the measures of two angles is that of a straight angle and if one of them is acute then the other should be _______.
Answer
(a) acute
(b) obtuse (if the angle is less than 180°)
(c) straight
(d) acute
(e) an obtuse angle.
 
Question 8
Find the measure of the angle shown in each figure. (First estimate with your eyes and then find the actual measure with a protractor).

Answer
The angle measures
(i)$30^0$
(ii)$120^0$
(iii)$60^0$
(iv)$180^0$
 
Question 9
Find the angle measure between the hands of the clock in each figure:

Answer
90°, 30°, 180°
 
Question 10
Investigate
In the given figure, the angle measures 30°. Look at the same figure through a magnifying glass.
Does the angle become larger? Does the size of the angle change?

Answer
The angle does not change
 
Question 11
Measure and classify each angle

Angle	Measure	Type
∠AOB	–	–
∠AOC	–	–
∠BOC	–	–
∠DOC	–	–
∠DOA	–	–
∠DOB	–	–

 
Answer

Angle	Measure	Type
∠AOB	50	Acute
∠AOC	130	Obtuse
∠BOC	80	Acute
∠DOC	100	Obtuse
∠DOA	145	Obtuse
∠DOB	180	Straight

 
 

Section 6

Question 1.
Which of the following are models for perpendicular lines?
(a) The adjacent edges of a table top.
(b) The lines of a railway track.
(c) The line segments forming the letter ‘L’.
(d) The letter V.
Answer
(a)Perpendicular
(b) Not perpendicular
(c) Perpendicular
(d) Not perpendicular
 
Question 2.
Let PQ be the perpendicular to the line segment XY. Let PQ and XY intersect in the point A. What is the measure of ∠PAY?
Answer
90
 
Question 3
There are two set-squares in your box. What are the measures of the angles that are formed at their corners? Do they have any angle measure that is common?
Answer
One is a 30° – 60° – 90° set square; the other is a 45° – 45° – 90° set square.
The angle of measure 90° (i.e. a right angle) is common between them.
 
Question 4.
Study the diagram. The line l is perpendicular to line m

(a) Is CE = EG?
(b) Does PE bisect CG?
(c) Identify any two-line segments for which PE is the perpendicular bisector.
(d) Are these true?
(i) AC > FG
(ii) CD = GH
(iii) BC < EH.
Answer
(a) Yes, as same units
(b) Yes, as CE =EG
(c) BH, DF
(d) All are true.
(i)True, (ii) True, (iii) True
 
 

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