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
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiawU_JvkgJA1xL3WbFROtIC1JQclU8cQU8duYICOk_YAdpZ2T1YPgqrtQQoZE2SufBE1WGdxfROmX1UJ1JnL7G7q6BEb3vDAXlEZKgciU70eQS0n8RbhnS8IaDGi5H7j45Lvuvs2ueNboOAej3sfsuXIkEhpsSKTU3IPO7ZB8G2s9Kwb2kn-3TnC4W/w273-h178/Class%20-%2010%20Chapter%20-%2011%20Constructions%20%20Exercise%20-%2011.2%20img%2012.JPG)
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°
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmovyJQjkZaGGGh3Duf74oHBd4RZQAgEM2lCWEPhFp1qXjqbCycwGUZucBQbG9Hg_YQrUY5Bp5wYY21u02xpqoLmlDiMUaoFjpkyO8ExtqslQoYKcY1R2CVZgqWDJu-itBRUTdzN0ViTg2JpFewY38n59g8VVaetPNWg5-XlO2IGaqI4N2Z0a66e8M/s1600/Class%20-%2010%20Chapter%20-%2011%20Constructions%20%20Exercise%20-%2011.2%20img%2013.JPG)
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°
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-u7Sh8MQV2E0tEXqhpX1QrlL_pFrd030th1CC568ISgGmFs8vOGwtE4w_LH4fJWJOiwm8GQymf7RJYUjbpB_ZO7j2dTIMF5V91jWVJJN75_BP79ei6mi4vNLMiwBrdmoZRHqM9hWc7dE-syYZCy0oIgWOsrwJbrIKsxPyCgybUkz1duhxs4rwXXb5/w238-h201/Class%20-%2010%20Chapter%20-%2011%20Constructions%20%20Exercise%20-%2011.2%20img%2014.JPG)
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°
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_b-QbisAC_h02KUMWbpRsm7Leknglg4dhEiWuSTNcVCeMfCrgqsz3bjin8eHYeHZ0ed7-zw-dynGdpKcoru4rHpuDuP0A6yd7ImObCbBjuMgsBtowPI1CfDluxGrAMLpLANHmDYftG_i_EK27a6NFIlPkRPOhgKAQ-DaVpOURjqokrRolTh8MOajU/s1600/Class%20-%2010%20Chapter%20-%2011%20Constructions%20%20Exercise%20-%2011.2%20img%2015.JPG)
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°
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggQb3BjMZ2PLvpIiCE8_IEK9Dmj1JWtlJcvbX94oj83FVupiT2teb-mi7UoPx_uHUcKw8h7tCb9KacNCBdaGlb3s0_YGdOTupySoDlZB74AjwF5TvS7q07YzZPOc_ccBk78Ac6kZNXPISYGb0y-_kSsH2d2XPhHV29VTyBmXZxtNkVVVMM7HkCiinr/s1600/Class%20-%2010%20Chapter%20-%2011%20Constructions%20%20Exercise%20-%2011.2%20img%2016.JPG)
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°
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2WFe5AC0Eaea8OpJ_bIGvWmed6MynpiPwsieICF29ZVo3aYl1mUpOC9ksrF1c-RpzEOHhCHzk6QHd69D0iSd1k2h-LXmZIRHJB0h8kJmmTv-sRQB8TiYtkayBDfcG6dZfhNbCSwqm8uNsN7rxGDe80mAAPZBFV-tPrdqVoo_SqcnUiaS5LrWhIpLV/s1600/Class%20-%2010%20Chapter%20-%2011%20Constructions%20%20Exercise%20-%2011.2%20img%2017.JPG)
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)°