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Chapter 11 Constructions RS Aggarwal Solution for Class 9th Maths

GeometricalConstructions


Exercise 12A

Question 1:

Steps of Construction:

  1. Draw a line segment AB = 5 cm
  2. With A as centre and radius equal to more than half of AB, draw two arcs, one above AB and the other below AB.
  3. With B as a centre and the same radius draw two arcs which cuts the previously drawn arcs at C and D.
  4. Join CD , intersecting AB at point P.

∴ CD is the perpendicular bisector of AB at the point P.

Question 2:

Step of Construction:

  1. Draw a line segment OA.
  2. AT A, draw ∠AOE=90 , using ruler and compass.
  3. With B as centre and radius more than half of BD, draw an arc.
  4. With D as centre and same radius draw another arc which cuts the previous arc at F.
  5. Join OF. ∴ ∠AOF=45 .
  6. Now with centre B and radius more than half of BC, draw an arc.
  7. With centre C and same radius draw another arc which cuts the previously drawn arc at X.
  8. Join OX. ∴ OX is the bisector of ∠AOF.


Question 3:

Step of Construction:

  1. Draw a line segment OA.
  2. With O as centre and any suitable radius draw an arc, cutting OA at B.
  3. With B as centre and the same radius cut the previously drawn arc at C.
  4. With C as centre and the same radius cut the arc at D.
  5. With C as centre and the radius more than half CD draw an arc.
  6. With D as centre and the same radius draw another arc which cuts the previous arc at E.
  7. Join E Now, ∠AOE =900
  8. Now with B as centre and radius more than half of CB draw an arc.

(iv) With C as centre and same radius draw an arc which cuts the previous at F.

  1. Join OF.
  2. ∴ F is the bisector of right ∠AOE.

Question 4:

Step of construction:

  1. Draw a line segment BC=5cm.
  2. With B as centre and radius equal to BC draw an arc.
  3. With C as centre and the same radius draw another arc which cuts the previous arc at A.
  4. Join AB and AC.

Then ∆ABC is the required equilateral triangle.

Question 5:

Question 6:

Question 7:

Question 8:

Question 9:

Question 10:

Question 11:

Question 12:

Question 13:

Steps of Construction:

    1. Draw BC = 4.5 cm.
    2. Construct ∠CBX = 600
    3. Along BX set off BP =8cm.
    4. Join CP.
    5. Draw the perpendicular bisector of CP to intersecting BP at A.
    6. Join AC. ∴ ∆ABC is the required triangle.

Question 14:

Steps of Construction:

  1. Draw BC = 5.2 cm.
  2. Construct ∠CBX = 300
  3. Set off BP = 3.5 cm.
  4. Join PC.
  5. Draw the right bisector of PC, meeting BP produced at A.
  6. Join AC. ∴ ∆ABC is the required triangle.

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