RS Aggarwal Class 6 Math Fourteen Chapter Constructions (Using Ruler And Pair of Compasses) Exercise 14A Solution
EXERCISE 14A
(1) Draw a line segment PQ = 6.2 cm. Draw the perpendicular bisector of PQ.
Ans: Steps for construction:
(i) Draw a line segment PQ, which is equal 6.2 cm.
(ii) With P as the center and radius more than half of PQ, draw arcs, one on each side of PQ.
(iii) With Q as the center and the same radius as before, draw arcs cutting the previously drawn arcs at A and B, respectively.
(iv) Draw AB, meeting PQ at R.
(2) Draw a line segment AB = 5.6 cm. Draw the particular bisector of AB.
Ans: Steps for construction:
(i) Draw a line segment AB = 5.6 cm.
(ii) With A as the center and radius more than half of AB. Draw arc, one on each side of Ab.
(iii) With B as the center and the same radius as before, draw arcs cutting the previously drawn arcs at P and Q respectively.
(iv) draw PQ meeting AB at R.
(3) Draw an angle equal to ANGLE AOB, given in the adjoining figure.
Ans: Here ANGLE AOB is given.
(i) Draw a ray QP.
(ii) With O as the center and any suitable radius, draw an arc cutting OA and OB at C and E respectively.
(iii) With Q as the center and the same radius draw an arc cutting QP at D.
(iv) With D as the center and radius equal to CE, cut the arc through D at F.
(v) Draw QP and produce it to point R.
(4) Draw an angle of 50o with the help of a protractor. Draw a ray bisecting this angle.
Ans: Steps for construction:
(i) Draw ∠BAC = 50o with help of protractor.
(ii) With A as the center and any convent radius, draw an arc cutting AB and AC at Q and P.
(iii) With P as the center and radius more than half of PQ. Draw an arc.
(iv) With Q as the center and the same radius as before, draw another arc cutting the previously drawn.
(v) Draw SA and produced it to point R. Then, ray AR bisects ∠BAC.
(5) Construct ∠AOB = 85o with the help of a protractor. Draw a ray OX bisecting ∠AOB.
Ans: Steps for construction:
(i) Draw ∠ AOC = 85o with the help a protractor.
(ii) With O as the center and ray convenient radius, draw an arc cutting OA and OB at P and Q.
(iii) With P as the center and radius more than half of PQ, draw an arc.
(iv) With Q as the center the same radius as before, draw another arc cutting the previously drawn arc at a point R.
(v) Draw RO and produced it to point X.
Then, ray OX bisects ∠AOB.
(6) Draw a line AB. Take a point P on it. Draw a line passing through P and perpendicular to AB.
Ans: Steps for construction:
(i) Draw a line ab.
(ii) Take a point P on AB.
(iii) With P as the center, draw an arc of any radius, which intersects line AB at M and N, respectively.
(iv) With M as the center and radius more than half of MN, draw an arc.
(v) With N as the center and the same radius as the same radius as in step (iv), draw an arc that cuts the previously drawn arc at R.
(vi) Draw PR.
PR is the required line, which is perpendicular to AB.
(7) Draw a line AB. Take a point outside it. Draw a line passing through P and perpendicular to AB.
Ans: Draw a line AB.
(ii) Take a point P outside AB.
(iii) With P as the center and a convenient radius, ddraw an arc intersecting AB at M and N, respectively.
(iv) With M as the center and radius more than half of MN, ddraw an arc.
(v) With N as the center and the same radius, draw an arc cutting the previously drawn arc at Q.
(vi) draw PQ meeting AB at S.
PQ is the required line that passes through P and is perpendicular to AB.
(8) Draw a line AB. Take a point P outside it. Draw a line passing through P and parallel to AB.
Ans: Steps for construction:
(i) Draw a line AB.
(ii) Take a point P outside AB and another point O on AB.
(iii) Draw PO.
(iv) draw ∠FPO such that ∠FPO is equal to AOP.
(v) Extend FP to E.
Then, the line EF passes though the point P and EFIIAB.
(9) Draw ∠ABC of measure 60o such that AB = 4.5 cm and BC = 5 cm. Through C draw a line parallel to AB and through B draw a line parallel to AC, intersecting each other at D. Measure BD and CD.
Ans: Steps for construction:
(i) Draw a line BX and take a point A. such that AB is equal to 4.5 cm.
(ii) Draw ∠ABP = 60o with the help[ of protractor.
(iii) With A as the center and a radius of 5 cm, draw an arc cutting PB at C.
(iv) Draw AC.
(v) Now, draw ∠BCY = 60o
(vi) Then, draw ∠ABW, such that ∠ABW is equal to ∠CAX, which cut the ray CY at D.
(vii) Draw BD.
When we measure BD and CD, we have:
BD = 5 cm and CD = 4.5 cm
(10) Draw a line segment AB = 6 cm. Take a point C on AB such that AC = 2.5 cm. Draw CD perpendicular to AB.
Ans: Steps for construction:
(i) Draw a line segment AB, which is equal to 6 cm.
(ii) Take a point C on AB such that AC is equal to 2.5 cm.
(iii) With C as the center, draw an arc cutting AB at M and N.
(iv) With M as the center and radius more than half of MN, draw an arc.
(v) With N as the and the same radius as before, draw another arc cutting the previously drawn arc at S.
(vi) Draw SC and produce it to D.
(11) Draw a line segment AB = 5.6 cm. Draw the right bisector of AB.
Ans: Steps for construction:
(i) Draw a line segment AB, which is equal to 5.6 cm.
(ii) With A as the center and radius more than half of AB, draw arcs, one on each side of AB.
(iii) With B as the center and the same radius as before, draw arcs cutting the previously drawn arc at M and N, respectively.
(iv) Draw MN, meeting AB at R.
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