RS Aggarwal MCQs: Geometrical Constructions Notes | EduRev

Mathematics (Maths) Class 9

Class 9 : RS Aggarwal MCQs: Geometrical Constructions Notes | EduRev

 Page 1


Question:1
Draw a line segment AB = 5.6 cm and draw its perpendicular bisector. Measure the length of each part.
Solution:
Steps of Construction
1. Draw a line AB = 5.6 cm.
2. With A as centre and radius more than half of AB, draw one above and other below line AB. 
3. Similarly, with B as centre draw two arcs cutting the previous drawn arcs and name the points obtained as M and
N respectively.
4. Join MN intersecting AB at point O. 
MN is the required perpendicular bisector. 
AO = OB = 2.8 cm
Question:2
Draw an angle of 80° with the help of a protractor and bisect it. Measure each part of the bisected angle.
Solution:
Steps of construction
1. Draw ?
AOB = 80° using protractor. 
2. With O as centre and a convenient radius, draw an arc cutting AO at N and OB at M. 
3. With N as centre and a convenient radius, draw an arc. 
4. Similarly, with M as centre and same radius, cut the previous drawn arc and name it as point C. 
5. Join OC.
OC is the required angle bisector. 
On measuring we get
?
AOC = ?
BOC = 40°
 
Question:3
Construct an angle of 90° using ruler and compasses and bisect it.
Solution:
Page 2


Question:1
Draw a line segment AB = 5.6 cm and draw its perpendicular bisector. Measure the length of each part.
Solution:
Steps of Construction
1. Draw a line AB = 5.6 cm.
2. With A as centre and radius more than half of AB, draw one above and other below line AB. 
3. Similarly, with B as centre draw two arcs cutting the previous drawn arcs and name the points obtained as M and
N respectively.
4. Join MN intersecting AB at point O. 
MN is the required perpendicular bisector. 
AO = OB = 2.8 cm
Question:2
Draw an angle of 80° with the help of a protractor and bisect it. Measure each part of the bisected angle.
Solution:
Steps of construction
1. Draw ?
AOB = 80° using protractor. 
2. With O as centre and a convenient radius, draw an arc cutting AO at N and OB at M. 
3. With N as centre and a convenient radius, draw an arc. 
4. Similarly, with M as centre and same radius, cut the previous drawn arc and name it as point C. 
5. Join OC.
OC is the required angle bisector. 
On measuring we get
?
AOC = ?
BOC = 40°
 
Question:3
Construct an angle of 90° using ruler and compasses and bisect it.
Solution:
Steps of construction:
1. Draw a line segment AB.
2. With A as the centre and and a small radius, draw an  arc cutting AB at M.
3. With M as the centre and the same radius as above, draw an arc cutting the previously drawn arc at N.
4. With N as the centre and the same radius as above, draw an arc cutting the previously drawn arc at P.
5. Again, with N as the centre and a radius more than half of PN, draw an arc.
6. With P as the centre and the same radius as above, draw an arc cutting the previously drawm arc at Q.
7. Join AQ cutting the arc at O and produced it to C.
8. With O as the centre and a radius more than half of OM, draw an arc.
9. With M as the centre and the same radius as above, draw another arc cutting the previously drawn arc at point R.
10. Join AR.
Thus, AR bisects ?
BAC.
Question:4
Construct each of the following angles, using ruler and compasses:
i
75°
ii
37.5°
iii
135°
iv
105°
v
22.5°
Solution:
i
 75°
Steps of construction
1. Draw a line XY.
2. Take a point O on XY. 
3. With O as centre, draw a semi circle, cutting XY at P and Q.
4. Construct ?
YOR = 90°
.
5. Draw the bisector of ?
YOR = 90°
 cutting the semi circle at point S. 
6. With S and T as centres draw two arcs intersecting at point A. 
Page 3


Question:1
Draw a line segment AB = 5.6 cm and draw its perpendicular bisector. Measure the length of each part.
Solution:
Steps of Construction
1. Draw a line AB = 5.6 cm.
2. With A as centre and radius more than half of AB, draw one above and other below line AB. 
3. Similarly, with B as centre draw two arcs cutting the previous drawn arcs and name the points obtained as M and
N respectively.
4. Join MN intersecting AB at point O. 
MN is the required perpendicular bisector. 
AO = OB = 2.8 cm
Question:2
Draw an angle of 80° with the help of a protractor and bisect it. Measure each part of the bisected angle.
Solution:
Steps of construction
1. Draw ?
AOB = 80° using protractor. 
2. With O as centre and a convenient radius, draw an arc cutting AO at N and OB at M. 
3. With N as centre and a convenient radius, draw an arc. 
4. Similarly, with M as centre and same radius, cut the previous drawn arc and name it as point C. 
5. Join OC.
OC is the required angle bisector. 
On measuring we get
?
AOC = ?
BOC = 40°
 
Question:3
Construct an angle of 90° using ruler and compasses and bisect it.
Solution:
Steps of construction:
1. Draw a line segment AB.
2. With A as the centre and and a small radius, draw an  arc cutting AB at M.
3. With M as the centre and the same radius as above, draw an arc cutting the previously drawn arc at N.
4. With N as the centre and the same radius as above, draw an arc cutting the previously drawn arc at P.
5. Again, with N as the centre and a radius more than half of PN, draw an arc.
6. With P as the centre and the same radius as above, draw an arc cutting the previously drawm arc at Q.
7. Join AQ cutting the arc at O and produced it to C.
8. With O as the centre and a radius more than half of OM, draw an arc.
9. With M as the centre and the same radius as above, draw another arc cutting the previously drawn arc at point R.
10. Join AR.
Thus, AR bisects ?
BAC.
Question:4
Construct each of the following angles, using ruler and compasses:
i
75°
ii
37.5°
iii
135°
iv
105°
v
22.5°
Solution:
i
 75°
Steps of construction
1. Draw a line XY.
2. Take a point O on XY. 
3. With O as centre, draw a semi circle, cutting XY at P and Q.
4. Construct ?
YOR = 90°
.
5. Draw the bisector of ?
YOR = 90°
 cutting the semi circle at point S. 
6. With S and T as centres draw two arcs intersecting at point A. 
?
AOY = 75°.  
 
ii
37.5°
Steps of construction
1. Draw a line XY.
2. Take a point O on XY. 
3. With O as centre, draw a semi circle, cutting XY at P and Q.
4. Construct ?
YOR = 90°
.
5. Draw the bisector of ?
YOR = 90°
 cutting the semi circle at point S. 
6. With S and T as centres draw two arcs intersecting at point A. 
7. Draw the angle bisector of ?
AOY. 
8. ?
BOY is the required angle of  37.5°. 
iii
 135°
Steps of construction:
1. Draw a line XY.
2. Take a point A on XY.
3. With A as centre, draw a semi circle, cutting XY at P and Q.
4. Construct ?
YAC = 90°
.
5. Draw AB, bisector of ?
XAC.
Thus, ?
YAB = 135°
iv
 105°
Page 4


Question:1
Draw a line segment AB = 5.6 cm and draw its perpendicular bisector. Measure the length of each part.
Solution:
Steps of Construction
1. Draw a line AB = 5.6 cm.
2. With A as centre and radius more than half of AB, draw one above and other below line AB. 
3. Similarly, with B as centre draw two arcs cutting the previous drawn arcs and name the points obtained as M and
N respectively.
4. Join MN intersecting AB at point O. 
MN is the required perpendicular bisector. 
AO = OB = 2.8 cm
Question:2
Draw an angle of 80° with the help of a protractor and bisect it. Measure each part of the bisected angle.
Solution:
Steps of construction
1. Draw ?
AOB = 80° using protractor. 
2. With O as centre and a convenient radius, draw an arc cutting AO at N and OB at M. 
3. With N as centre and a convenient radius, draw an arc. 
4. Similarly, with M as centre and same radius, cut the previous drawn arc and name it as point C. 
5. Join OC.
OC is the required angle bisector. 
On measuring we get
?
AOC = ?
BOC = 40°
 
Question:3
Construct an angle of 90° using ruler and compasses and bisect it.
Solution:
Steps of construction:
1. Draw a line segment AB.
2. With A as the centre and and a small radius, draw an  arc cutting AB at M.
3. With M as the centre and the same radius as above, draw an arc cutting the previously drawn arc at N.
4. With N as the centre and the same radius as above, draw an arc cutting the previously drawn arc at P.
5. Again, with N as the centre and a radius more than half of PN, draw an arc.
6. With P as the centre and the same radius as above, draw an arc cutting the previously drawm arc at Q.
7. Join AQ cutting the arc at O and produced it to C.
8. With O as the centre and a radius more than half of OM, draw an arc.
9. With M as the centre and the same radius as above, draw another arc cutting the previously drawn arc at point R.
10. Join AR.
Thus, AR bisects ?
BAC.
Question:4
Construct each of the following angles, using ruler and compasses:
i
75°
ii
37.5°
iii
135°
iv
105°
v
22.5°
Solution:
i
 75°
Steps of construction
1. Draw a line XY.
2. Take a point O on XY. 
3. With O as centre, draw a semi circle, cutting XY at P and Q.
4. Construct ?
YOR = 90°
.
5. Draw the bisector of ?
YOR = 90°
 cutting the semi circle at point S. 
6. With S and T as centres draw two arcs intersecting at point A. 
?
AOY = 75°.  
 
ii
37.5°
Steps of construction
1. Draw a line XY.
2. Take a point O on XY. 
3. With O as centre, draw a semi circle, cutting XY at P and Q.
4. Construct ?
YOR = 90°
.
5. Draw the bisector of ?
YOR = 90°
 cutting the semi circle at point S. 
6. With S and T as centres draw two arcs intersecting at point A. 
7. Draw the angle bisector of ?
AOY. 
8. ?
BOY is the required angle of  37.5°. 
iii
 135°
Steps of construction:
1. Draw a line XY.
2. Take a point A on XY.
3. With A as centre, draw a semi circle, cutting XY at P and Q.
4. Construct ?
YAC = 90°
.
5. Draw AB, bisector of ?
XAC.
Thus, ?
YAB = 135°
iv
 105°
Steps of construction
 
1. Draw a line XY.
2. Take a point O on XY.
3. With O as centre, draw a semi circle, cutting XY at P and Q.
4. Construct ?
YOS = 90°
.
5. Draw RO, bisector of ?
XOS.
6. Draw AO, bisector of ?
ROS. 
?
AOY = 105° is the required angle. 
v
 22.5°
Steps of construction:
1. Draw a ray AB.
2. Draw an angle ?
BAE = 45°
.
3. With A as the centre and a small radius, draw an arc cutting AB at P and AE at Q.
4. With P as the centre and a radius more than half of PQ, draw an arc.
5. With Q as the centre and the same radius as above, draw another arc cutting the previously drawn arc at D.
6. Join AD.
Thus, ?
BAC is the required angle of measure 22.5
o
.
Question:5
Construct a ?ABC in which BC = 5 cm, AB = 3.8 cm and AC = 2.6 cm. Bisect the largest angle of this triangle.
Solution:
Steps of construction:
1. Draw a line segment BC = 5 cm.
2. With B as the centre and a radius equal to 3.8 cm, draw an arc.
Page 5


Question:1
Draw a line segment AB = 5.6 cm and draw its perpendicular bisector. Measure the length of each part.
Solution:
Steps of Construction
1. Draw a line AB = 5.6 cm.
2. With A as centre and radius more than half of AB, draw one above and other below line AB. 
3. Similarly, with B as centre draw two arcs cutting the previous drawn arcs and name the points obtained as M and
N respectively.
4. Join MN intersecting AB at point O. 
MN is the required perpendicular bisector. 
AO = OB = 2.8 cm
Question:2
Draw an angle of 80° with the help of a protractor and bisect it. Measure each part of the bisected angle.
Solution:
Steps of construction
1. Draw ?
AOB = 80° using protractor. 
2. With O as centre and a convenient radius, draw an arc cutting AO at N and OB at M. 
3. With N as centre and a convenient radius, draw an arc. 
4. Similarly, with M as centre and same radius, cut the previous drawn arc and name it as point C. 
5. Join OC.
OC is the required angle bisector. 
On measuring we get
?
AOC = ?
BOC = 40°
 
Question:3
Construct an angle of 90° using ruler and compasses and bisect it.
Solution:
Steps of construction:
1. Draw a line segment AB.
2. With A as the centre and and a small radius, draw an  arc cutting AB at M.
3. With M as the centre and the same radius as above, draw an arc cutting the previously drawn arc at N.
4. With N as the centre and the same radius as above, draw an arc cutting the previously drawn arc at P.
5. Again, with N as the centre and a radius more than half of PN, draw an arc.
6. With P as the centre and the same radius as above, draw an arc cutting the previously drawm arc at Q.
7. Join AQ cutting the arc at O and produced it to C.
8. With O as the centre and a radius more than half of OM, draw an arc.
9. With M as the centre and the same radius as above, draw another arc cutting the previously drawn arc at point R.
10. Join AR.
Thus, AR bisects ?
BAC.
Question:4
Construct each of the following angles, using ruler and compasses:
i
75°
ii
37.5°
iii
135°
iv
105°
v
22.5°
Solution:
i
 75°
Steps of construction
1. Draw a line XY.
2. Take a point O on XY. 
3. With O as centre, draw a semi circle, cutting XY at P and Q.
4. Construct ?
YOR = 90°
.
5. Draw the bisector of ?
YOR = 90°
 cutting the semi circle at point S. 
6. With S and T as centres draw two arcs intersecting at point A. 
?
AOY = 75°.  
 
ii
37.5°
Steps of construction
1. Draw a line XY.
2. Take a point O on XY. 
3. With O as centre, draw a semi circle, cutting XY at P and Q.
4. Construct ?
YOR = 90°
.
5. Draw the bisector of ?
YOR = 90°
 cutting the semi circle at point S. 
6. With S and T as centres draw two arcs intersecting at point A. 
7. Draw the angle bisector of ?
AOY. 
8. ?
BOY is the required angle of  37.5°. 
iii
 135°
Steps of construction:
1. Draw a line XY.
2. Take a point A on XY.
3. With A as centre, draw a semi circle, cutting XY at P and Q.
4. Construct ?
YAC = 90°
.
5. Draw AB, bisector of ?
XAC.
Thus, ?
YAB = 135°
iv
 105°
Steps of construction
 
1. Draw a line XY.
2. Take a point O on XY.
3. With O as centre, draw a semi circle, cutting XY at P and Q.
4. Construct ?
YOS = 90°
.
5. Draw RO, bisector of ?
XOS.
6. Draw AO, bisector of ?
ROS. 
?
AOY = 105° is the required angle. 
v
 22.5°
Steps of construction:
1. Draw a ray AB.
2. Draw an angle ?
BAE = 45°
.
3. With A as the centre and a small radius, draw an arc cutting AB at P and AE at Q.
4. With P as the centre and a radius more than half of PQ, draw an arc.
5. With Q as the centre and the same radius as above, draw another arc cutting the previously drawn arc at D.
6. Join AD.
Thus, ?
BAC is the required angle of measure 22.5
o
.
Question:5
Construct a ?ABC in which BC = 5 cm, AB = 3.8 cm and AC = 2.6 cm. Bisect the largest angle of this triangle.
Solution:
Steps of construction:
1. Draw a line segment BC = 5 cm.
2. With B as the centre and a radius equal to 3.8 cm, draw an arc.
3. With C as the centre and a radius equal to 2.6 cm, draw an arc cutting the previously drawn arc at A.
4. Join AB and AC.
Thus, ABC is the required triangle.
Take the largest angle and draw the angle bisector.
Question:6
Construct a ?ABC in which BC = 4.8 cm, ?B = 45° and ?C = 75°. Measure ?A.
Solution:
Steps of construction:
1. Draw a line segment BC = 4.8 cm.
2. Construct ?
CBX = 45°
.
3. Construct ?
BCY = 75°
.
4. The ray BX and CY intersect at A.
Thus, ?
ABC is the required triangle.
When we measure ?
A, we get ?
A = 60°
.
Question:7
Construct an equilateral triangle each of  whose sides measures 5 cm.
Solution:
Steps of construction:
1. Draw a line segment AB = 5 cm.
2. With A as the centre and a radius equal to AB, draw an arc.
3. With B as the centre and the same radius as above, draw another arc cutting the previously drawn arc at C.
4. Join AC and BC.
Thus, ?
ABC is the required triangle.
Question:8
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