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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, ABO and a Line segment QR
2. With center A and any radius, draw an arc which intersects ∠BAC at E and O
3. With center Q and same radius draw arc which intersect QR at S.
4. With center S and radius equal to DE, draw an arc which intersect previous arc at T
5. Draw a line segment joining Q and T
∴ ∠PQR = ∠BAC
Draw an obtuse angle, Bisect it. Measure each of the angles so obtained.
1. Draw angle ABC of 120°
2. With center B and any radius, draw an arc which intersects AB at P and BC at Q
3. With center P and Q and radius more than 1/2 PQ, draw two arcs, with intersect each other at R.
4. Join BR
∴ ∠ABB = ∠RBC = 60°
Using your protractor, thaw an angle of measure 108°. With this angle as given, draw an angle of 54°.
1. Draw an angle ABC of 108°
3. With center P and Q and radius more than 2 PQ, draw two arcs, which intersect each
other at R.
∴ ∠RBC = 54°
Using protractor, draw a right angle. Bisect it to get an angle of measure 45°.
1. Draw an angle ABC of 90°
3. With center P and Q and radius more than 1/2 PQ, draw two arcs, which intersect each 2 other at R.
4. Join RB
∴ ∠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 angle DCA and DCB forming Linear pair
2. With center C and any radius, draw an arc which intersects AC at P, CD at Q and CB at R.
3. With center P and Q and any radius draw two arcs which interest each other at S
4. Join SC
5. With center Q and R any radius draw two arcs, which intersect each other at T.
6. Join TC
∠SCT = 90° [By using protractor]
Draw a pair of vertically opposite angles. Bisect each of the two angles. Verify that the bisecting rays are in the same line.
1. Draw a pair of vertically opposite angle AOC and DOB
2. With center 0 and any radius drawn two arcs which intersect OA at P, Q - OB at S and OD at R.
3. With center P and Q and radius more than 1/2 PQ, draw two arcs which intersect each other at U.
4. Join to
5. With center R and S radius more than 1/2 RS, draw two arcs which intersect each other at U.
6. Join OU.
∴ TOU is a straight line
Using ruler and compasses only, draw a right angle.
1. Draw a line segment AB
2. With center A and any radius draw arc which intersect AB at C.
3. With center C and same radius draw an arc which intersects AB at C.
4. With center D and same radius draw arc which intersect arc in (2) at E.
5. With centers E and C and any radius, draw two arcs which intersect each other at F.
6. Join FA
∠FAB = 90°
Using ruler and compasses only, draw an angle of measure 135°.
1. Draw a line segment AB and produce BA to point C.
2. With center A and any radius draw arc which intersect AC at D and AB at E.
3. With center D and E and radius more than 1/2 DE, draw two arcs which intersect each other at F.
4. Join FA which intersect the arc in (2) at G.
5. With centers G and D and radius more than 1/2 GD, draw two arcs which intersect each other at H.
6. Join HA
∴ ∠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 angle ABC of 72° with the help of protractor.
2. With center B and any radius, draw an arc which intersect AB at D and BC at E.
4. Join FB which intersect the arc in (2) at G.
5. With centers D and G and radius more than 1/2 DE, draw two arcs which intersect each other at F.
6. With centers D and G and radius more than n 1/2 DG draw two arcs which intersect each other at H
7. Join HB
∴ ∠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:
2. With center A and any radius drawn an arc which intersect AC at D and AB at E.
3. With center D and E and radius more than 1/2 DE, draw arcs cutting each other at F.
4. Join FA which intersect arc in (2) at G.
5. With centers G and E and radius more than 1/2 GE, draw arcs cutting each other at H.
∴ ∠HAB = 45°
(ii) Steps of construction:
1. Draw a line segment AB.
2. With center A and any radius draw in arc which intersect AB at C.
3. With center C and same radius thaw an arc which intersects previous arc at D.
4. With centers D same radius draw an arc which intersects are in (2) at E.
5. With centers E and D same radius more than 1/2 ED draw an arc cutting each other at F.
∴ ∠FAB = 90°
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Chapter 11: Constructions? Exercise – 11.1...
Chapter 11: Constructions? Exercise – 11.3...