Chapter 5 Plane Geometry and Line and Angle Ex 5.3

Rajasthan Board RBSE Class 9 Maths Solutions Chapter 5 Plane Geometry and Line and Angle Ex 5.3

Question 1.
Draw a line segment AB = 10 cm. Bisect this line segment and verify by measuring the lengths of the two segments.
Solution.
Construction:
1. Draw a line segment AB = 10 cm
2. With A and B as centres and a radius more than half of AB, draw arcs on both side of the line segment AB, cutting each other at M and N respectively.
RBSE Solutions for Class 9 Maths Chapter 5 Plane Geometry and Line and Angle 1
3. Join MN which intersect AB at L. Hence, L bisect AB.
By measuring we can say AL = BL = 5 cm.
Question 2.
Construct an angle of 120° . Bisect the angle and verify by measuring the two angles.
Solution.
Steps of Construction:
1. Draw a line segment of any measure named as PQ.
2. With P as centre draw an angle of 120° with the help of protractor.
RBSE Solutions for Class 9 Maths Chapter 5 Plane Geometry and Line and Angle 2
3. With P as centre again draw an arc which cuts line segments PQ and PS at M and N.
4. With M and N as centres and with radius little more than half the arc, draw arcs cutting each other at T. Join PT which is the required bisector of ∠SPQ = 120°.
∴ ∠TPQ = ∠TPS = 60° (each)
Question 3.
Draw an angle of 40° using protractor. Now, with the help of ruler and compass, construct an angle equal to this angle.
Solution.
Steps of Construction:
1. Draw ∠BAC = 40° with the help of protractor. By taking A as centre draw an arc which cuts AB and AC at P & Q.
RBSE Solutions for Class 9 Maths Chapter 5 Plane Geometry and Line and Angle 3
2. Now take O as centre on another line segment EF and taking the same radius PQ draw an arc which cuts OF at R. Now again take R as centre and draw the arc which cut at S.
3. Join O to S which is the required ∠ROS = 40°.
Question 4.
Draw a line segment of length 6 cm. From a point P outside this line, draw a perpendicular on this line.
Solution.
Steps of construction:
1. First of all draw a line segment AB = 6 cm
RBSE Solutions for Class 9 Maths Chapter 5 Plane Geometry and Line and Angle 4
2. Take a point P (outside the line) and draw an arc in such a way that its cuts AB into two points C and D. Again by taking C & D as centre take suitable arc and draw two arc which intersect at Q. Join PQ.
Hence, PQ is the required perpendicular on AB from P.
Question 5.
Construct ∠ABC = 120°. Through A draw a line parallel to BC.
Solution.
Steps of construction:
1. Draw a line segment BC of any measure.
2. By taking B as centre, draw an angle of 120° with the help of compass and ruler.
3. Now at A, we will draw a line parallel to BC by making 60° at A.
RBSE Solutions for Class 9 Maths Chapter 5 Plane Geometry and Line and Angle 5
(Reason: Lines are parallel if sum of the interior angles on the same side of transversal is 180°)
Question 6.
Draw a line segment of length 9 cm using ruler and compass. Divide this line segment into three equal parts.
Solution.
Steps of construction:
1. Draw a line segment AB = 9 cm.
2. Make any acute angle at A.
3. Starting from A as centre and any convenient radius set off three equal distances.
4. Join the third arc to B.
5. Then we will draw line segments parallel to EB.
RBSE Solutions for Class 9 Maths Chapter 5 Plane Geometry and Line and Angle 6
Hence AC = CD = DB = 3 cm each.
Question 7.
Draw a line segment of length 10 cm. Using ruler and compass divide this segment in the ratio 3 : 2. Measure the length of these segments.
Solution.
Steps of construction:
1. Draw any line segment say AB = 10 cm
2. At A, draw a ray AY making an acute angle YAB.
3. Using compass mark five points on AY such that
AP = PQ = QR = RS = ST.
4. Join TB.
5. Through point R draw a line parallel to TB i.e RL which divides AB in the ratio 3 : 2.
RBSE Solutions for Class 9 Maths Chapter 5 Plane Geometry and Line and Angle 7
On measuring AB we find that AL = 6 cm and LB = 4 cm.
Question 8.
Draw a line segment AB of length 6 cm, using ruler and compass divide this in the ratio 1:2:3.
Solution.
Steps of construction:
1. Draw a line segment AB = 6 cm.
2. Make any acute angle at A. i.e. ∠CAB.
3. Starting from A as centre and any convenient radius set off 6 equal distances.
4. Join 6th arc to B.
5. Then we will draw line segment PM and QN parallel to OB.
RBSE Solutions for Class 9 Maths Chapter 5 Plane Geometry and Line and Angle 8
Hence AN : NM : MB =1:2:3.
Question 9.
Using ruler and compass, construct the following angles.
(i) 150°
(ii) 105°
(iii) 75°
Solution.
Steps of Construction
(i) 150° = 189° – \frac { 1 }{ 2 } x 60 = 180° – 30°
First draw ∠AOC = 60° then draw the bisector of ∠AOC.
Hence ∠BOP = 150° is the required angle.
RBSE Solutions for Class 9 Maths Chapter 5 Plane Geometry and Line and Angle 9
(ii) Let OB be a line segment and at O construct an angle of 90°. With this vertical line construct an angle of 15° which gives required ∠BOP = 105°.
RBSE Solutions for Class 9 Maths Chapter 5 Plane Geometry and Line and Angle 9.1
(iii) Let OB be a straight line and at O draw an angle of 60° and 90° then draw bisector of these two angles, which is the required ∠BOP = 75°.
RBSE Solutions for Class 9 Maths Chapter 5 Plane Geometry and Line and Angle 9.2

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