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Draw an angle and label it as ∠BAC. Construct another angle, equal to ∠BAC
Steps of construction:
1. Draw an angle ABC and a line segment QR.
2. With center A and any radius, draw an arc which intersects ∠BAC at E and D.
3. With Q as a centre and same radius draw an arc which intersects QR at S.
4. With S as center and radius equal to DE, draw an arc which intersects the previous arc at T.
5. Draw a line segment joining Q and T.
Therefore ∠PQR = ∠BAC
Draw an obtuse angle. Bisect it. Measure each of the angles so formed.
1. Draw an angle ∠ABC of 120°.
2. With B as a centre and any radius, draw an arc which intersects AB at P and BC at Q.
3. With P as center and radius more than half of PQ draw an arc.
4. With Q as a center and same radius draw an arc which cuts the previous arc at R.
5. Join BR.
Therefore ∠ABR = ∠RBC = 60°
Using your protractor, draw an angle of 108°. With this given angle as given, draw an angle of 54°.
1. Draw an angle ABC of 108°.
2. With B as the center and any radius draw an arc which intersects AB at P and BC at Q.
4. With Q as the centre and same radius draw an arc which intersects the previous arc at R.
Therefore ∠RBC = 54°
Using the protractor, draw a right angle. Bisect it to get an angle of measure 45°.
1. Draw an angle ABC of 90°.
2. With B as the centre and any radius draw an arc which intersects AB at P and BC at Q.
4. With Q as center and same radius draw an arc which intersects the previous arc at R.
5. Join RB.
Therefore ∠RBC = 45°
Draw a linear pair of angles. Bisect each of the two angles. Verify that the two bisecting rays are perpendicular to each other.
1. Draw two angles DCA and DCB forming linear pair
2. With center C and any radius draw an arc which intersects AC at P and CD at Q and CB at R
3. With center P and Q and any radius draw two arcs which intersect each other at S
4. Join SC
5. With Q and R as center and any radius draw two arcs which intersect each other at T
6. Join TC
Therefore ∠SCT = 90°.
Draw a pair of vertically opposite angles. Bisect each of the two angles. Verify that the bisecting rays are in the same line.
Steps of Construction:
1. Draw a pair of vertically opposite angle ∠AOC and ∠DOB.
2. Keeping O as the center and any radius draw two arcs which intersect OA at P, OC at Q, OB at S and OD at R.
3. Keeping P and Q as center and radius more than half of PQ draw two arcs which intersect each other at T.
4. Join TO.
5. Keeping R and S as center and radius more than half of RS draw two arcs which intersect each other at U.
6. Join OU.
Therefore TOU is a straight line
Using rulers and compasses only, draw a right angle.
1. Draw a line segment AB.
2. Keeping A as the center and any radius draw an arc which intersects AB at C.
3. Keeping C as center and the same radius draw an arc which intersects the previous arc at D.
4. Keeping D as the center and same radius draw an arc which intersects arc in (2) at E.
5. Keeping E and D as center and radius more than half of ED draw arcs which intersect each other at F.
6. Join FA.
Therefore ∠FAB = 90°
Using rulers and compasses only, draw an angle of measure 135°.
1. Draw a line segment AB and produce BA to C.
2. Keeping A as the center and any radius draw an arc which intersects AC at D and AB at E.
3. Keeping D and E as center and radius more than half of DE draw arcs which intersect each other at F.
4. Join FA which intersects the arc in (2) at G.
5. Keeping G and D as center and radius more than half of GD draw arcs which intersect each other at H.
6. Join HA.
Therefore ∠HAB = 135°
Using a protractor, draw an angle of measure 72°. With this angle as given draw angles of measure 36° and 54°.
1. Draw an ∠ABC of 720 with the help of a protractor.
2. Keeping B as center and any radius draw an arc which intersects AB at D and BC at E.
3. Keeping D and E as center and radius more than half of DE draw two arcs which intersect each other at F.
4. Join FB which intersects the arc in (2) at G.
5. Keeping D and G as center and radius more than half of DG draw two arcs which intersect each other at H
6. Join HB
Therefore ∠HBC = 54° ∠FBC = 36°
Construct the following angles at the initial point of a given ray and justify the construction:
(i) 45°
(ii) 90°
(i) Steps of construction:
5. Keeping G and E as center and radius more than half of GE draw arcs which intersect each other at H.
Therefore ∠HAB = 45°
(ii) Steps of construction
Construct the angles of the following measurements:
(i) 30°
(ii) 75°
(iii) 105°
(iv) 135°
(v) 15°
(vi) 22(1/2)°
2. Keeping A as the centre and any radius draw an arc which intersects AB at C.
4. Keeping D and C as center and radius more than half of DC draw arcs which intersect each other at E.
5. Join EA.
Therefore ∠EAB = 30°
(ii) Steps of construction:
1. Draw a line segment AB
2. Keeping A as center and any radius draw an arc which intersects AB at C
3. Keeping C as center and the same radius draw an arc which intersects the previous arc at D
4. Keeping D as center and same radius draw an arc which intersects arc in (2) at E
5. Keeping E and D as center and radius more than half of ED, draw arcs intersecting each other at F
6. Join FA which intersects arc in (2) at G
7. Keeping G and D as center and radius more than half of GD draw arcs intersecting each other at H
8. Join HA
Therefore ∠HAB = 75°
(iii) Steps of construction:
4. Keeping D as the centre and same radius draw an arc which intersects arc in (2) at E.
6. Join FA which intersects arc in (2) at G.
7. Keeping E and G as center and radius more than half of EG draw arcs which intersect each other at H.
8. Join HA.
Therefore ∠HAB = 105°
(iv) Steps of construction:
5. Keeping G and D as center and radius more than half of GD draw arcs which intersect each other at H
(v) Steps of construction:
5. Join EA which intersects arc in (2) at F.
6. Keeping F and C as center and radius more than half of FC draw arcs which intersect each other at G.
7. Join GA.
Therefore ∠GAB = 15°
(vi) Steps of construction:
5. Keeping E and D as center and radius more than half of ED draw arcs which intersect each at F.
7. Keeping G and C as center and radius more than half of GC draw arcs intersecting each other at point H.
8. Join HA which intersects the arc in (2) at a point I.
9. Keeping I and C as center and radius more than half of IC draw arcs intersecting each other at point J.
10. Join JA.
Therefore ∠JAB = 22(1/2)°
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Chapter 17: Constructions Exercise – 17.1...
Chapter 17: Constructions Exercise – 17.3...