| Exercise 14.1 Exercise 14.2 Exercise 14.3 Exercise 14.4 Exercise 14.5 Exercise 14.6 |
NCERT Answers for Class 6 Maths
Chapter 14 Practical Geometry Exercise 14.6
Page 291
Ex 14.6 Class 6 Maths Question 1. Draw ∠ POQ of measure 75° and find its line of symmetry.
Answer
Step 1: Draw a line I and mark a point O on it.
Step 2: Place the pointer of the compasses at O and draw an arc of any radius which intersects the line I at A.
Step 3: Taking same radius, with centre A, cut the previous arc at B.
Step 4: Join 0B, then ∠ BOA = 60°.
Step 5: Taking same radius, with centre B, cut the previous arc at C.
Step 6: Draw bisector of ∠ BOC. The angle is of 90°. Mark it at D. Thus, ∠ DOA = 90°
Step 7: Draw OP as bisector of Z DOB. Thus, ∠ POA= 75°
Ex 14.6 Class 6 Maths Question 2. Draw an angle of measure 147° and construct its bisector.
Answer
Step 1: Draw a ray OA
Step 2: With the help of protractor, construct ∠ AOB = 147°.
Step 3: Taking centre O and any convenient radius, draw an arc which intersects the arms OA and OB at P and Q respectively.
Step 4: Taking P as centre and radius more than half of PQ, draw an arc.
Step 5: Taking Q as centre and with the same radius, draw another arc which intersects the previous at R.
Step 6: Join OR and produce it.
Step 7: Thus, OR is the required bisector of ∠ AOB.
Ex 14.6 Class 6 Maths Question 3. Draw a right angle and construct its bisector.
Answer
Steps of construction:
Step 1: Draw a line PQ and take a point O on it.
Step 2: Taking O as centre and convenient radius, draw an arc which intersects PQ at A and B.
Step 3: Taking A and B as centres and radius more than half of AB, draw two arcs which intersect each other at C.
Step 4: Join OC. Thus, ∠ COQ is the required right angle.
Step 5: Taking B and E as centre and radius more than half of BE, draw two arcs which intersect each other at the point D.
Step 6: Join OD . Thus, OD is the required bisector of ∠ COQ.
Ex 14.6 Class 6 Maths Question 4. Draw an angle of measure 153° and divide it into four equal parts.
Answer
Steps of construction:
Step 1: Draw a ray OA .
Step 2: At O, with the help of a protractor, construct ∠ AOB = 153°
Step 3: Draw OC as the bisector of ∠ AOB.
Step 4: Again, draw OD as bisector of ∠ AOC.
Step 5: Again, draw OE as bisector of ∠ BOC.
Step 6: Thus, OC, OD and OE divide ∠ AOB in four equal parts.
Ex 14.6 Class 6 Maths Question 5. Construct with ruler and compasses, angles of following measures: (a) 60° (b) 30° (c) 90° (d) 120° (e) 45° (f) 135°
Answer
(a) 60°
Step 1: Draw a ray OA
Step 2: Taking O as centre and convenient radius, mark an arc, which intersects OA at P.
Step 3: Taking P as centre and same radius, cut previous arc at Q.
Step 4: Join OQ. Thus, ∠ BOA is required angle of 60°.
(b) 30°
Step 1: Draw a ray OA
Step 2: Taking O as centre and convenient radius, mark an arc, which intersects OA at P.
Step 3: Taking P as centre and same radius, cut previous arc at Q.
Step 4: Join OQ. Thus, ∠ BOA is required angle of 60°
Step 5: Put the pointer on P and mark an arc.
Step 6: Put the pointer on Q and with same radius, cut the previous arc at C.
Step 7: Thus, ∠ COA is required angle of 30°.
(c) 90°
Step 1: Draw a ray OA.
Step 2: Taking O as centre and convenient radius, mark an arc, which intersects OA at X.
Step 3: Taking X as centre and same radius, cut previous arc at Y.
Step 4:Taking Y as centre and same radius, draw another arc intersecting the same arc at Z.
Step 4: Join OS and produce it to form a ray OB.
Thus, ∠ BOA is required angle of 90°
(d) 120°
Step 1: Draw a ray OA
Step 2: Taking O as centre and convenient radius, mark an arc, which intersects OA at P.
Step 3: Taking P as centre and same radius, cut previous arc at Q.
Step 4: Taking Q as centre and same radius cut the arc at S. Join OS.
Thus, ∠ AOD is required angle of 120°
(e) 45°
Step 1: Draw a ray OA.
Step 2: Taking O as centre and convenient radius, mark an arc, which intersects OA at X.
Step 3: Taking X as centre and same radius, cut previous arc at Y
Step 4: Taking Y as centre and same radius, draw another arc intersecting the same arc at Z.
Step 5: Taking Y and Z as centres and same radius, draw two arcs intersecting each other at S.
Step 5: Join OS and produce it to form a ray OB. Thus, ∠ BOA is required angle of 90°
Step 6: Draw the bisector of ∠ BOA. Thus, ∠ MOA is required angle of 45°
(f) 135°
Step 1: Draw a line PQ and take a point O on it.
Step 2: Taking O as centre and convenient radius, mark an arc, which intersects PQ at A
Step 3: Taking A and B as centres and radius more than half of AB, draw two arcs intersecting each other at R.
Step 4: Join OR. Thus, ∠ QOR= ∠POQ = 90°
Step 5: Draw OD the bisector of ∠ POR.
Thus, ∠ QOD is required angle of 135°
Ex 14.6 Class 6 Maths Question 6. Draw an angle of measure 45° and bisect it.
Answer
Steps of construction:
Step 1: Draw a line PQ and take a point O on it.
Step 2: Taking O as centre and a convenient radius, draw an arc which intersects PQ at two points A and B.
Step 3: Taking A and B as centres and radius more than half of AB, draw two arcs which intersect each other at C.
Step 4: Join OC. Then ∠ COQ is an angle of 90°
Step 5: Draw OE as the bisector of ∠ COE. Thus, ∠ QOE = 45°
Step 6: Again draw OG as the bisector of ∠ QOE. Thus, ∠ QOG = ∠ EOG = 22½°
Ex 14.6 Class 6 Maths Question 7. Draw an angle of measure 135° and bisect it.
Answer
Steps of construction:
Step 1: Draw a line PQ and take a point O on it.
Step 2: Taking O as centre and convenient radius, mark an arc, which intersects PQ at A and B.
Step 3: Taking A and B as centres and radius more than half of AB, draw two arcs intersecting each other at R. Join OR.
Step 4: Thus, ∠ QOR= ∠ POQ= 90°
Step 5: Draw OD the bisector of ∠ POR.
Thus, ∠ QOD is required angle of 135°
Step 6: Now, draw OE as the bisector of ∠ QOD.
Thus, ∠ QOE = ∠ DOE = 67½°
Ex 14.6 Class 6 Maths Question 8. Draw an angle of 70O. Make a copy of it using only a straight edge and compasses.
Answer
Steps of construction:
Draw an angle 700 with protractor, i.e., ∠POQ = 70°
Draw a ray AB.
Place the compasses at O and draw an arc to cut the rays of ∠ POQ at L and M.
Use the same compasses, setting to draw an arc with A as centre, cutting AB at X.
Set your compasses setting to the length LM with the same radius.
Place the compasses pointer at X and draw the arc to cut the arc drawn earlier at Y.
Join AY. Thus, ∠ YAX= 70°
Ex 14.6 Class 6 Maths Question 9. Draw an angle of 40O. Copy its supplementary angle.
Answer
Steps of construction:
(a) Draw an angle of 40° with the help of protractor, naming ∠ AOB.
Draw a line PQ.
Take any point M on PQ.
Place the compasses at O and draw an arc to cut the rays of ∠ AOB at L and N.
Use the same compasses setting to draw an arc M as centre, cutting MQ at X.
Set your compasses to length LN with the same radius.
Place the compasses at X and draw the arc to cut the arc drawn earlier Y.
Join MY. Thus, ∠ QMY = 40° and ∠ PMY is supplementary of it.