Advertisement

Rectilinear Figures ML Aggarwal ICSE Class-9 Chapter-13

APC Understanding Mathematics Exercise-13 Rectilinear Figures Solved Questions

Rectilinear Figures ML Aggarwal ICSE Class-9 Maths Chapter-13. Step by Step Answer of Exercise-13.1, Exercise-13.2, MCQ and Chapter-Test of  Rectilinear Figures Questions for ICSE Class-9 Understanding APC Mathematics. Visit official website CISCE for detail information about ICSE Board Class-9.

Rectilinear Figures ML Aggarwal ICSE Class-9 Maths Chapter-13


–: Select Topics :–

Exercise-13.1 , 

Advertisement

Exercise-13.2, 

 MCQ ,

Chapter-Test , 

Note:- Before viewing Solution of Chapter -13 Rectilinear Figures Class-9 of ML Aggarwal Solutions.  Read the Chapter Carefully then solve all example given in Exercise-13.1, Exercise-13.2.The Chapter-13  Rectilinear Figures of ML Aggarwal Class-9 is Main Chapter in Class 9 Mathematics.


Exercise – 13.1 Solutions of Rectilinear Figures for ICSE Class-9

Question 1.

If two angles of a quadrilateral are 40° and 110° and the other two are in the ratio 3 : 4, find these angles.

Answer 1

 

Question 2.

If the angles of a quadrilateral, taken inorder, are in the ratio 1 : 2 : 3 : 4, prove that it is a trapezium.

Answer 2

 

Advertisement

Question 3.

If an angle of a parallelogram is two-thirds of its adjacent angle, find the angles of the parallelogram.

Answer 3

 

Question 4.

 

(a) In figure (1) given below, ABCD is a parallelogram in which ∠DAB = 70°, ∠DBC = 80°. Calculate angles CDB and ADB.(b) In figure (2) given below, ABCD is a parallelogram. Find the angles of the AAOD.(c) In figure (3) given below, ABCD is a rhombus. Find the value of x.

Answer 4

 

Question 5.

(a) In figure (1) given below, ABCD is a parallelogram with perimeter 40. Find the values of x and y.

(b) In figure (2) given below. ABCD is a parallelogram. Find the values of x and y.

(c) In figure (3) given below. ABCD is a rhombus. Find x and y.

Answer 5

 

Question 6.

The diagonals AC and BD of a rectangle > ABCD intersect each other at P. If ∠ABD = 50°, find ∠DPC.

Answer 6

 

Advertisement

Question 7.

(a) In figure (1) given below, equilateral triangle EBC surmounts square ABCD. Find angle BED represented by x.

(b) In figure (2) given below, ABCD is a rectangle and diagonals intersect at O. AC is produced to E. If ∠ECD = 146°, find the angles of the ∆ AOB.

(c) In figure (3) given below, ABCD is rhombus and diagonals intersect at O. If ∠OAB : ∠OBA = 3:2, find the angles of the ∆ AOD.

Answer  7

 

Question 8.

 

(a) In figure (1) given below, ABCD is a trapezium. Find the values of x and y.

(b) In figure (2) given below, ABCD is an isosceles trapezium. Find the values of x and.y.

(c) In figure (3) given below, ABCD is a kite and diagonals intersect at O. If ∠DAB = 112° and ∠DCB = 64°, find ∠ODC and ∠OBA.Answer 8

 

Question 9.

(i) Prove that each angle of a rectangle is 90°.
(ii) If the angle of a quadrilateral are equal, prove that it is a rectangle.
(iii) If the diagonals of a rhombus are equal, prove that it is a square.
(iv) Prove that every diagonal of a rhombus bisects the angles at the vertices.

Answer 9

 

Question 10.

ABCD is a parallelogram. If the diagonal AC bisects ∠A, then prove that:
(i) AC bisects ∠C
(ii) ABCD is a rhombus
(iii) AC ⊥ BD.

Answer 10

 

Question 11.

(i) Prove that bisectors of any two adjacent angles of a parallelogram are at right angles.

(ii) Prove that bisectors of any two opposite angles of a parallelogram are parallel.

(iii) If the diagonals of a quadrilateral are equal and bisect each other at right angles, then prove that it is a square.

Answer 11

 

Question 12.

(i) If ABCD is a rectangle in which the diagonal BD bisect ∠B, then show that ABCD is a square.
(ii) Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.

Answer 12

 

Question 13.

P and Q are points on opposite sides AD and BC of a parallelogram ABCD such that PQ passes through the point of intersection O of its diagonals AC and BD. Show that PQ is bisected at O.

Answer 13

 

Question 14.

 

(a) In figure (1) given below, ABCD is a parallelogram and X is mid-point of BC. The line AX produced meets DC produced at Q. The parallelogram ABPQ is completed. Prove that:
(i) the triangles ABX and QCX are congruent;
(ii)DC = CQ = QP

(b) In figure (2) given below, points P and Q have been taken on opposite sides AB and CD respectively of a parallelogram ABCD such that AP = CQ. Show that AC and PQ bisect each other.

Answer  14

 

Question 15.

ABCD is a square. A is joined to a point P on BC and D is joined to a point Q on AB. If AP=DQ, prove that AP and DQ are perpendicular to each other.

Answer 15

 

Question 16.

If P and Q are points of trisection of the diagonal BD of a parallelogram ABCD, prove that CQ || AP.

Answer 16

 

Question 17.

A transversal cuts two parallel lines at A and B. The two interior angles at A are bisected and so are the two interior angles at B ; the four bisectors form a quadrilateral ABCD. Prove that
(i) ABCD is a rectangle.
(ii) CD is parallel to the original parallel lines.

Answer 17

 

Question 18.

In a parallelogram ABCD, the bisector of ∠A meets DC in E and AB = 2 AD. Prove that
(i) BE bisects ∠B
(ii) ∠AEB = a right angle.

Answer 

 

Question 19.

ABCD is a parallelogram, bisectors of angles A and B meet at E which lie on DC. Prove that AB

Answer 19

 

Question 20.

ABCD is a square and the diagonals intersect at O. If P is a point on AB such that AO =AP, prove that 3 ∠POB = ∠AOP.

Answer 20

 

Question 21.

ABCD is a square. E, F, G and H are points on the sides AB, BC, CD and DA respectively such that AE = BF = CG = DH. Prove that EFGH is a square.

Answer 21

 

Question 22.

(a) In the Figure (1) given below, ABCD and ABEF are parallelograms. Prove that
(i) CDFE is a parallelogram
(ii) FD = EC
(iii) Δ AFD = ΔBEC.
(b) In the figure (2) given below, ABCD is a parallelogram, ADEF and AGHB are two squares. Prove that FG = AC

Answer 22

 

Question 23.

ABCD is a rhombus in which ∠A = 60°. Find the ratio AC : BD.

Answer 23

 


Exercise 13.2 Rectilinear Figures ML Aggarwal Solutions

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 1

 

Question 2.

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

Answer 2

 

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 3

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 4

 

Question 5

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

Answer 5

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 6

 

Question 7.

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

Answer 7

 

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 8

Question 9.

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

Answer 9

 

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.

Advertisement

Answer 10

 

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 11

 

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 12

 

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 13

 

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 14

 

Question 15.

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

Answer 15:

 

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 16

 

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 17

 

Question 18.

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

Answer 18

 

Question 19. Rectilinear Figures ML Aggarwal 

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

Answer 19

 

Question 20.

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

Answer 20:

 

Question 21.

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

Answer 21

 

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 22

 

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 23

 

Question 24.

Construct a regular hexagon of side 2.5 cm.

Answer 24

 


MCQ of Rectilinear Figures for ICSE Class-9 ML Aggarwal

Choose the correct answer from the given four options (1 to 12):

Question 1.

Three angles of a quadrilateral are 75°, 90° and 75°. The fourth angle is
(a) 90°
(b) 95°
(c) 105°
(d) 120°

Answer 1

Sum of 4 angles of a quadrilateral = 360° Sum of three angles = 75° + 90° + 75° = 240° Fourth angle = 360° – 240° = 120° (d)

Question 2.

A quadrilateral ABCD is a trapezium if
(a) AB = DC
(b) AD = BC
(c) ∠A + ∠C = 180°
(d) ∠B + ∠C = 180°

Answer 2

A quadrilateral ABCD is a trapezium if ∠B + ∠C= 180°
(Sum of co-interior angles) (d)

Question 3.

If PQRS is a parallelogram, then ∠Q – ∠S is equal to
(a) 90°
(b) 120°
(c) 0°
(d) 180°

Answer 3

PQRS is a parallelogram ∠Q – ∠S = 0
(∵ Opposite angles of a parallelogram, are equal) (c)

Question 4.

A diagonal of a rectangle is inclined to one side of the rectangle at 25°. The acute angle between the diagonals is
(a) 55°
(b) 50°
(c) 40°
(d) 25°

Answer 4

In a rectangle a diagonal is inclined to one side of the rectangle is 25°

Question 5.


ABCD is a rhombus such that ∠ACB = 40°. Then ∠ADB is
(a) 40°
(b) 45°
(c) 50°
(d) 60°

Answer 5

 

Question 6.


The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O. If ∠D AC = 32° and ∠AOB = 70°, then ∠DBC is equal to
(a) 24°
(b) 86°
(c) 38°
(d) 32°

Answer 6

 

 

Question 7.


If the diagonals of a square ABCD intersect each other at O, then ∆OAB is
(a) an equilateral triangle
(b) a right angled but not an isosceles triangle
(c) an isosceles but not right angled triangle
(d) an isosceles right angled triangle

Answer 

 

Question 8.


If the diagonals of a quadrilateral PQRS bisect each other, then the quadrilateral PQRS must be a
(a) parallelogram
(b) rhombus
(c) rectangle
(d) square

Answer 8

Diagonals of a quadrilateral PQRS bisect each other, then quadrilateral must be a parallelogram.
(∵ A rhombus, rectangle and square are also parallelogram) (a)

Question 9.


If the diagonals of a quadrilateral PQRS bisect each other at right angles, then the quadrilateral PQRS must be a
(a) parallelogram
(b) rectangle
(c) rhombus
(d) square

Answer 9


Diagonals of quadrilateral PQRS bisect each other at right angles, then quadrilateral PQRS [ must be a rhombus.
(∵ Square is also a rhombus with each angle equal to 90°) (c)

Question 10.

Which of the following statement is true for a parallelogram?
(a) Its diagonals are equal.
(b) Its diagonals are perpendicular to each other.
(c) The diagonals divide the parallelogram into four congruent triangles.
(d) The diagonals bisect each other.

Answer 10


For a parallelogram an the statement ‘The diagoanls bisect each other’ is true. (d)

Question 11.

Which of the following is not true for a parallelogram?
(a) opposite sides are equal
(b) opposite angles are equal
(c) opposite angles are bisected by the diagonals
(d) diagonals bisect each other

Answer 11

The statement that in a parallelogram, .the opposite angles are bisected by the diagonals, is not true in each case. (c)

Question 12.

A quadrilateral in which the diagonals are equal and bisect each other at right angles is a
(a) rectangle which is not a square
(b) rhombus which is not a square
(c) kite which is not a square
(d) square

Answer 12

In a quadrilateral, if diagonals are equal and bisect each other at right angles, is a square. (d)


Chapter Test of Exercise -13 Rectilinear Figures for ML Aggarwal Solutions

Question 1.

In the given figure, ABCD is a parallelogram. CB is produced to E such that BE=BC. Prove that AEBD is a parallelogram.

Answer 1

 

Question 2.

In the given figure, ABC is an isosceles triangle in which AB=AC. AD bisects exterior angle PAC and CD || BA. Show that
(i) ∠DAC=∠BCA
(ii) ABCD is a parallelogram.

Answer 2

 

Question 3.

Prove that the quadrilateral obtained by joining the mid-points of an isosceles trapezium is a rhombus.

Answer 3

 

Question 4.

Find the size of each lettered angle in the Following Figures.

Answer 4

 

Question 5

Find the size of each lettered angle in the following figures :

Answer 5

 

Question 6.

In the adjoining figure, ABCD is a rhombus and DCFE is a square. If ∠ABC = 56°, find
(i) ∠DAG
(ii) ∠FEG
(iii) ∠GAC
(iv) ∠AGC.

Answer 6

 

Question 7.

If one angle of a rhombus is 60° and the length of a side is 8 cm, find the lengths of its diagonals.

Answer 7

 

Question 8.

Using ruler and compasses only, construct a parallelogram ABCD with AB = 5 cm, AD = 2.5 cm and ∠BAD = 45°. If the bisector of ∠BAD meets DC at E, prove that ∠AEB is a right angle.

Answer 8

 

–: end of Rectilinear Figures :–

Return to ML Aggarawal Maths Solutions for ICSE  Class-9.


Thanks

 

Share with your friends

Show Comments (2)
Insert math as
Block
Inline
Additional settings
Formula color
Text color
#333333
Type math using LaTeX
Preview
\({}\)
Nothing to preview
Insert