ML Aggarwal Rectilinear Figures Exe-13.2 Class 9 ICSE Maths Solutions Ch-13. Step by Step Solutions of Exercise-13.2 Rectilinear Figures of ML Aggarwal for ICSE Class 9th Mathematics Questions. Visit official website CISCE for detail information about ICSE Board Class-9.

## ML Aggarwal Rectilinear Figures Exe-13.2 Class 9 ICSE Maths Solutions

Board | ICSE |

Subject | Maths |

Class | 9th |

Chapter-13 | Rectilinear Figures |

Topics | Solution of Exe-13.2 Questions |

Academic Session | 2024-2025 |

### Rectilinear Figures

ML Aggarwal Rectilinear Figures Exe-13.2 Class 9 ICSE Maths Solutions Ch-13

**Question 1. ****Using ruler and compasses only, construct the quadrilateral ABCD in which ∠ BAD = 45°, AD = AB = 6cm, BC = 3.6cm, CD = 5cm. Measure ∠ BCD.**

**Answer : ****Construction:**

(i) Draw a line segment AB = 6cm

(ii) At A, draw a ray AX making an angle of 45^{o} and cut off AD = 6cm

(iii) With centre B and radius 3.6 cm and with centre D and radius 5 cm, draw two arcs intersecting each other at C.

(iv) Join BC and DC.

ABCD is the required quadrilateral.

On measuring ∠BCD, it is 60^{o}

**Question 2. ****Draw a quadrilateral ABCD with AB = 6cm, BC = 4cm, CD = 4 cm and ∠ ABC = ∠ BCD = 90°**

**Answer : ****Construction:**

(i) Draw a line segment BC = 4 cm

(ii) At B and C draw rays BX and CY making an angle of 90^{o} each

(iii) From BX, cut off BA = 6 cm and from CY, cut off CD = 4cm

(iv) Join AD.

ABCD is the required quadrilateral.

**Question 3. ****Using ruler and compasses only, construct the quadrilateral ABCD given that AB = 5 cm, BC = 2.5 cm, CD = 6 cm, ∠BAD = 90° and the diagonal AC = 5.5 cm.**

**Answer : ****Construction:**

(i) Draw a line segment AB = 5cm

(ii) With centre A and radius 5.5cm and with centre B and radius 2.5cm draw arcs which intersect each other at C.

(iii) Join AC and BC.

(iv) At A, draw a ray AX making an angle of 90^{o}.

(v) With centre C and radius 6cm, draw an arc intersecting AX at D

(vi) Join CD.

ABCD is the required quadrilateral.

**Question 4. ****Construct a quadrilateral ABCD in which AB = 3.3 cm, BC = 4.9 cm, CD = 5.8 cm, DA = 4 cm and BD = 5.3 cm.**

**Answer : ****Construction:**

(i) Draw a line segment AB = 3.3cm

(ii) with centre A and radius 4cm, and with centre B and radius 5.3cm, draw arcs intersecting each other at D.

(iii) Join AD and BD.

(iv) With centre B and radius 4.9 cm and with centre D and radius 5.8cm, draw arcs intersecting each other at C.

(v) Join BC and DC.

ABCD is the required quadrilateral.

**Question 5. ****Construct a trapezium ABCD in which AD || BC, AB = CD = 3 cm, BC = 5.2cm and AD = 4 cm**

**Answer : ****Construction:**

(i) Draw a line segment BC = 5.2cm

(ii) From BC, cut off BE = AD = 4cm

(iii) With centre E and C, and radius 3 cm, draw arcs intersecting each other at D.

(iv) Join ED and CD.

(v) With centre D and radius 4cm and with centre B and radius 3cm, draw arcs intersecting each other at A.

(vi) Join BA and DA

ABCD is the required trapezium.

**Question 6****. ****Construct a trapezium ABCD in which AD || BC, ∠B= 60°, AB = 5 cm. BC = 6.2 cm and CD = 4.8 cm.**

**Answer : ****Construction:**

(i) Draw a line segment BC = 6.2cm

(ii) At B, draw a ray BX making an angle of 60^{o} and cut off AB = 5cm

(iii) From A, draw a line AY parallel to BC.

(iv) With centre C and radius 4.8cm, draw an arc which intersects AY at D and D’.

(v) Join CD and CD’

ABCD and ABCD’ are the required two trapeziums.

**Question 7. ****Using ruler and compasses only, construct a parallelogram ABCD with AB = 5.1 cm, BC = 7 cm and ∠ABC = 75°.**

**Answer : ****Construction:**

(i) Draw a line segment BC = 7cm

(ii) A to B, draw a ray Bx making an angle of 75^{o} and cut off AB = 5.1cm

(iii) With centre A and radius 7cm with centre C and radius 5.1cm, draw arcs intersecting each other at D.

(iv) Join AD and CD.

ABCD is the required parallelogram.

**Question 8. ****Using ruler and compasses only, construct a parallelogram ABCD in which AB = 4.6 cm, BC = 3.2 cm and AC = 6.1 cm.**

**Answer : ****Construction:**

(i) Draw a line segment AB = 4.6cm

(ii) With centre A and radius 6.1cm and with centre B and radius 3.2cm, draw arcs intersecting each other at C.

(iii) Join AC and BC.

(iv) Again, with centre A and radius 3.2cm and with centre C and radius 4.6cm, draw arcs intersecting each other at C.

(v) Join AD and CD.

ABCD is the required parallelogram.

**Question 9. ****Using ruler and compasses, construct a parallelogram ABCD give that AB = 4 cm, AC = 10 cm, BD = 6 cm. Measure BC.**

**Answer : ****Construction:**

(i) Construct triangle OAB such that

OA = ½ x AC = ½ x 10cm = 5cm

OB = ½ x BD = ½ x 6cm = 3cm

As, diagonals of || gm bisect each other and AB = 4cm

(ii) Produce AO to C such that OA = OC = 5cm

(iii) Produce BO to D such that OB = OD = 3cm

(iv) Join AD, BC and CD

ABCD is the required parallelogram

(v) Measure BC which is equal to 7.2cm

**Question 10. ****Using ruler and compasses only, construct a parallelogram ABCD such that BC = 4 cm, diagonal AC = 8.6 cm and diagonal BD = 4.4 cm. Measure the side AB.**

**Answer :**

**Construction:**

(i) Construct triangle OBC such that

OB = ½ x BD = ½ x 4.4cm = 2.2cm

OC = ½ x AC = ½ x 8.6cm = 4.3cm

Since, diagonals of || gm bisect each other and BC = 4cm

(ii) Produce BO to D such that BO = OD = 2.2cm

(iii) Produce CO to A such that CO = OA = 4.3cm

(iv) Join AB, AD and CD

ABCD is the required parallelogram.

(v) Measure the side AB, AB = 5.6cm

**Question 11. ****Use ruler and compasses to construct a parallelogram with diagonals 6 cm and 8 cm in length having given the acute angle between them is 60°. Measure one of the longer sides.**

**Answer : ****Construction:**

(i) Draw AC = 6cm

(ii) Find the mid-point O of AC. **[Since, diagonals of || gm bisect each other]**

(iii) Draw line POQ such that POC = 60^{o} and OB = OD = ½ BD = ½ x 8cm = 4cm

So, from OP cut OD = 4cm and from OQ cut OB = 4cm

(iv) Join AB, BC, CD and DA.

ABCD is the required parallelogram.

(v) Measure the length of side AD = 6.1cm

**Question 12. ****Using ruler and compasses only, draw a parallelogram whose diagonals are 4 cm and 6 cm long and contain an angle of 75°. Measure and write down the length of one of the shorter sides of the parallelogram.**

**Answer : ****Construction:**

(i) Draw a line segment AC = 6cm

(ii) Bisect AC at O.

(iii) At O, draw a ray XY making an angle of 75^{o }at O.

(iv) From OX and OY, cut off OD = OB = 4/2 = 2cm

(v) Join AB, BC, CD and DA.

ABCD is the required parallelogram.

On measuring one of the shorter sides, we get AB = CD = 3cm

**Question 13. ****Using ruler and compasses only, construct a parallelogram ABCD with AB = 6 cm, altitude = 3.5 cm and side BC = 4 cm. Measure the acute angles of the parallelogram**

**Answer : ****Construction:**

(i) Draw AB = 6cm

(ii) At B, draw BP ⊥ AB

(iii) From BP, cut BE = 3.5cm = height of || gm

(iv) Through E draw QR parallel to AB

(v) With B as centre and radius BC = 4cm draw an arc which cuts QR at C.

(vi) Since, opposite sides of || gm are equal

So, AD = BC = 4cm

(vii)With A as centre and radius = 4cm draw an arc which cuts QR at D.

ABCD is the required parallelogram.

(viii) To measure the acute angle of parallelogram which is equal to 61^{o}.

**Question 14. ****The perpendicular distances between the pairs of opposite sides of a parallelogram ABCD are 3 cm and 4 cm and one of its angles measures 60°. Using ruler and compasses only, construct ABCD.**

**Answer : ****Construction:**

(i) Draw a straight-line PQ, take a point A on it.

(ii) At A, construct ∠QAF = 60^{o}

(iii) At A, draw AE ⊥ PQ from AE cut off AN = 3cm

(iv) Through N draw a straight line to PQ to meet AF at D.

(v) At D, draw AG ⊥ AD, from AG cut off AM = 4cm

(vi) Through M, draw at straight line parallel to AD to meet AQ in B and ND in C.

ABCD is the required parallelogram

**Question 15. ****Using ruler and compasses, construct a rectangle ABCD with AB = 5cm and AD = 3 cm.**

**Answer : ****Construction:**

(i) Draw a straight-line AB = 5cm

(ii) At A and B construct ∠XAB and ∠YBA = 90^{o}

(iii) From A and B cut off AC and BD = 3cm each

(iv) Join CD.

ABCD is the required rectangle.

**Question 16. ****Using ruler and compasses only, construct a rectangle each of whose diagonals measures 6cm and the diagonals intersect at an angle of 45°.**

**Answer : ****Construction:**

(i) Draw a line segment AC = 6cm

(ii) Bisect AC at O.

(iii) At O, draw a ray XY making an angle of 45^{o} at O.

(iv) From XY, cut off OB = OD = 6/2 = 3cm each

(v) Join AB, BC CD and DA.

ABCD is the required rectangle.

**Question 17. ****Using ruler and compasses only, construct a square having a diagonal of length 5cm. Measure its sides correct to the nearest millimeter.**

**Answer : ****Construction:**

(i) Draw a line segment AC = 5cm

(ii) Draw its percentage bisector XY bisecting it at O

(iii) From XY, cut off

OB = OD = 5/2 = 2.5cm

(iv) Join AB, BC, CD and DA.

ABCD is the required square

On measuring its sides, each = 3.6cm (approximate)

**Question 18. ****Using ruler and compasses only construct A rhombus ABCD given that AB 5cm, AC = 6cm measure ∠BAD.**

**Answer : ****Construction:**

(i) Draw a line segment AB = 5cm

(ii) With centre A and radius 6cm, with centre B and radius 5cm, draw arcs intersecting each other at C.

(iii) Join AC and BC

(iv) With centre A and C and radius 5cm, draw arc intersecting each other 5cm, draw arcs intersecting each other at D

(v) Join AD and CD.

ABCD is a rhombus

On measuring,

∠BAD = 106^{o}.

**Question 19. ****Using ruler and compasses only, construct rhombus ABCD with sides of length 4cm and diagonal AC of length 5 cm. Measure ∠ABC.**

**Answer : ****Construction:**

(i) Draw a line segment AC = 5cm

(ii) With centre A and C and radius 4cm, draw arcs intersecting each other above and below AC at D and B.

(iii) Join AB, BC, CD and DA.

ABCD is the required rhombus.

**Question 20. ****Construct a rhombus PQRS whose diagonals PR and QS are 8cip and 6cm respectively.**

**Answer : ****Construction:**

(i) Draw a line segment PR = 8cm

(ii) Draw its perpendicular bisector XY intersecting it at O.

(iii) From XY, cut off OQ = OS = 6/2 = 3cm each

(iv) Join PQ, QR, RS and SP

PQRS is the required rhombus.

**Question 21. ****Construct a rhombus ABCD of side 4.6 cm and ∠BCD = 135°, by using ruler and compasses only.**

**Answer :**

**Construction:**

(i) Draw a line segment BC = 4.6cm

(ii) At C, draw a ray CX making an angle of 135^{o} and cut off CD = 4.6cm

(iii) With centres B and D, and radius 4.6cm draw arcs intersecting each other at A.

(iv) Join BA and DA.

ABCD is the required rhombus.

**Question 22. ****Construct a trapezium in which AB || CD, AB = 4.6 cm, ∠ ABC = 90°, ∠ DAB = 120° and the distance between parallel sides is 2.9 cm.**

**Answer :**

**Construction:**

(i) Draw a line segment AB = 4.6cm

(ii) At B, draw a ray BZ making an angle of 90^{o} and cut off BC = 2.9cm

(iii) At C, draw a parallel line XY to AB.

(iv) At A, draw a ray making an angle of 120^{o} meeting XY at D.

ABCD is the required trapezium.

**Question 23. ****Construct a trapezium ABCD when one of parallel sides AB = 4.8 cm, height = 2.6cm, BC = 3.1 cm and AD = 3.6 cm.**

**Answer :**

**Construction:**

(i) Draw a line segment AB = 4.8cm

(ii) At A, draw a ray AZ making an angle of 90^{o} cut off AL = 2.6cm

(iii) At L, draw a line XY parallel to AB.

(iv) With centre A and radius 3.6cm and with centre B and radius 3.1cm, draw arcs intersecting XY at D and C respectively.

(v) Join AD and BC

ABCD is the required trapezium.

**Question 24. ****Construct a regular hexagon of side 2.5 cm.**

**Answer :**

**Construction:**

(i) With O as centre and radius = 2.5cm, draw a circle

(ii) take any point A on the circumference of circle.

(iii) With A as centre and radius = 2.5cm, draw an arc which cuts the circumference of circle at B.

(iv) With B as centre and radius = 2.5cm, draw an arc which cuts the circumference of circle at C.

(v) With C as centre and radius = 2.5cm, draw an arc which cuts the circumference of circle at D.

(vi) With D as centre and radius = 2.5cm, draw an arc which cuts the circumference of circle at E.

(vii) With E as centre and radius = 2.5cm, draw an arc which cuts the circumference of circle at F.

(viii) Join AB, BC, CD, DE, EF and FA.

(ix) ABCDEF is the required Hexagon.

— : End of ML Aggarwal Rectilinear Figures Exe-13.2 Class 9 ICSE Maths Solutions :–

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