RD Sharma Solutions Chapter 11 Constructions Exercise 11.2 Class 10 Maths
Chapter Name | RD Sharma Chapter 11 Constructions |
Book Name | RD Sharma Mathematics for Class 10 |
Other Exercises | - Exercise 11.1
- Exercise 11.3
|
Related Study | NCERT Solutions for Class 10 Maths |
Exercise 11.2 Solutions
1. Draw an angle and label it as ∠BAC. Construct another angle, equal to ∠BAC.
Solution
2. Draw an obtuse angle, Bisect it. Measure each of the angles so obtained.
Solution
3. Using your protractor, draw an angle of measure 108° . With this angle as given, draw an angle of 54° .
Solution
4. Using protractor, draw a right angle. Bisect it to get an angle of measure 45° .
Solution
5. Draw a linear pair of angles. Bisect each of the two angles. Verify that the two bisecting rays are perpendicular to each other.
Solution
6. Draw a pair of vertically opposite angles. Bisect each of the two angles. Verify that the bisecting rays are in the same line.
Solution
7. Using ruler and compasses only, draw a right angle.
Solution
Steps of construction : 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°
8. Using ruler and compasses only, draw an angle of measure 135° .
Solution
9. Using a protractor, draw an angle of measure 72° . With this angle as given, draw angles of measure 36° and 54° .
Solution
10. Construct the following angles at the initial point of a given ray and justify the construction :
(i) 45° (ii) 90°
Solution
11. Construct the angles of the following measurements: (i) 30°
(ii) 75°
(iii) 105°
(iv) 135°
(v) 15°
(vi) 22(1/2)°Solution
Steps of construction:
1. Draw a line segment AB.
2. With center A and any radius, draw an arc which intersect AB at C.
3. With center C and same radius, draw an arc which intersects previous arc at D.
4. With centers D and C and radius more than 1/2 DC, draw arcs intersecting each other at E
5. Join EA
∴ ∠EAB = 30°
Steps of construction:
1. Draw a line segment AB.
2. With center A any radius, draw an arc which intersect AB at C.
3. With center C and same radius, draw an arc which intersects previous arc at D.
4. With center D and same radius, draw an arc which interest are in (2) at E
5. With centers E and D and radius more than 1/2 ED, draw arcs intersecting each other at F.
6. Join FA which intersects arc in (2) at G.
7. With centers G and D, and radius more than 1/2 GD, draw arcs intersecting each other at H.
8. Join HA
∴ ∠HAB = 75°
Steps of construction:
1. Draw a line segment AB.
2. With center A and any radius, draw an arc which intersect AB at C.
3. With center C and same radius, draw an arc which intersects previous arc at D.
4. With center D and same radius, draw an arc which interest are in (2) at E
5. With centers E and D and radius more than 1/2 ED draw arcs intersecting each other at F.
6. Join FA which intersects arc in (2) at E
7. With centers E and G, and radius more than half of EG, draw arcs intersecting each
other at H.
8. Join HA
∠HAB = 105°
Steps of construction:
1. Draw a line segment AB and produce BA to pint C
2. With center A and any radius, draw an arc which intersect AC to D and AB at E.
3. With center D and E and radius more than half of DE, draw two arcs which intersects
each other at F.
4. Join FA which intersect the arc in (2) at G
5. With center G and D radius more than 1/2 GD draw two arcs which intersect each other at H
6. Join HA
∠HAB = 135°
Steps of construction:
Step 1: Draw a line segment AB
Step 2: with center A and any radius, draw an arc which intersects previous arc at C
Step 3: with center C and same radius, draw an arc which intersect previous arc at D
Step 4: with center D and C radius more than half of DC draw arcs intersecting each other
at E
Step 5: Join EA which intersects arc in (2) at F.
Step 6: With centers F and C and radius more than 1/2 FC draw arcs intersecting each other
Step 7: Join GA
∠GAB = 15°
Steps of construction:
Step 1: Draw a line segment AB
Step 2: with center A and any radius, draw an arc which intersects AB at C
Step 3: with center C and same radius, draw an arc which intersect previous arc at D
Step 4: with center D and same radius, draw an arc which intersects arc in (2) at E.
Step 5: with center E and D and radius more than half of ED, draw arcs intersecting each other at F.
Step 6: Join FA which intersects arc in (2) at G
Step 7: with center G and C and radius more than half of GC, draw arcs intersecting each other at H
Step 8: Join HA which intersects arc in (2) at 1.
Step 9: with centers I and C and radius more than half of IC, draw arcs intersecting each other
Step 10: Join JA
∴ ∠JAB = 22(1/2)°
