class 9 ncert maths ex11.1 3rd question
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Answer:
ex 11.1 Q 3=
Construct the angles of the following measurements:
(i)
(ii)
(iii)
Ans. (i) Steps of construction:
(a) Draw a ray OA.
(b) With O as centre and a suitable radius, draw an arc LM that cuts OA at L.
(c) With L as centre and radius OL, draw an arc to cut LM at N.
(d) Join O and N draw ray OB. Then AOB =
(e) With L as centre and radius greater than LN, draw an arc.
(f) Now with N as centre and same radius as in step 5, draw another arc cutting the arc drawn in step 5 at P.
(g) Join O and P and draw ray OC. Thus OC bisects AOB and therefore AOC = BOC =
(ii) Steps of construction:
(a) Draw a ray OA.
(b) With O as centre and convenient radius, draw an arc LM cutting OA at L.
(c) Now with L as centre and radius OL, draw an arc cutting the arc LM at P.
(d) Then taking P as centre and radius OL, draw an arc cutting arc PM at the point Q.
(e) Join OP to draw the ray OB. Also join O and Q to draw the OC. We observe that:
AOB = BOC =
(f) Now we have to bisect BOC. For this, with P as centre and radius greater than PQ draw an arc.
(g) Now with Q as centre and the same radius as in step 6, draw another arc cutting the arc drawn in step 6 at R.
(h) Join O and R and draw ray OD. Then AOD is the required angle of
(i) With L as centre and radius greater than LS, draw an arc.
(j) Now with S as centre and the same radius as in step 2, draw another arc cutting the arc draw in step 2 at T.
(k) Join O and T and draw ray OE. Thus OE bisects AOD and therefore AOE = DOE = .
(l) Let ray OE intersect the arc of circle at N.
(m) Now with L as centre and radius greater than LN, draw an arc.
(n) With N as centre and same radius as in above step and draw another arc cutting arc drawn in above step at I.
(o) Join O and I and draw ray OF. Thus OF bisects AOE and therefore AOF = EOF = .
(iii) Steps of construction:
(a) Draw a ray OA.
(b) With O as centre and a suitable radius, draw an arc LM that cuts OA at L.
(c) With L as centre and radius OL, draw an arc to cut LM at N.
(d) Join O and N draw ray OB. Then AOB =
(e) With L as centre and radius greater than LN, draw an arc.
(f) Now with N as centre and same radius as in step 5, draw another arc cutting the arc drawn in step 5 at P.
(g) Join O and P and draw ray OC. Thus OC bisects AOB and therefore AOC = BOC = .
(h) Let ray OC intersects the arc of circle at point Q.
(i) Now with L as centre and radius greater than LQ; draw an arc.
(j) With Q as centre and same radius as in above step, draw another arc cutting the arc shown in above step at R.
(k) Join O and R and draw ray OS. Thus OS bisects AOC and therefore COS = AOS
ex 1.1 Q3=
is in the picture
