ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures

Exercise 13.1

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.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q1.1

Question 2.
If the angles of a quadrilateral, taken in order, are in the ratio 1 : 2 : 3 : 4, prove that it is a trapezium.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q2.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q2.2

Question 3.
If an angle of a parallelogram is two-thirds of its adjacent angle, find the angles of the parallelogram.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q3.1

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.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q4.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q4.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q4.3

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.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q5.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q5.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q5.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q5.4

Question 6.
The diagonals AC and BD of a rectangle > ABCD intersect each other at P. If ∠ABD = 50°, find ∠DPC.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q6.1

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.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q7.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q7.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q7.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q7.4

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.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q8.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q8.2
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q8.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q8.4

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.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q9.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q9.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q9.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q9.4
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q9.5

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.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q10.1

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.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q11.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q11.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q11.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q11.4
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q11.5
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q11.6

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.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q12.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q12.2

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.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q13.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q13.2

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.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q14.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q14.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q14.3

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.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q15.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q15.2

Question 16.
If P and Q are points of trisection of the diagonal BD of a parallelogram ABCD, prove that CQ || AP.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q16.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q16.2

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.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q17.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q17.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q17.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q17.4
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q17.5
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q17.6
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q17.7

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.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q18.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q18.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q18.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q18.4

Question 19.
ABCD is a parallelogram, bisectors of angles A and B meet at E which lie on DC. Prove that AB
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q19.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q19.2

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.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q20.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q20.2

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.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q21.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q21.2

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
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q22.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q22.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q22.3

Question 23.
ABCD is a rhombus in which ∠A = 60°. Find the ratio AC : BD.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q23.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q23.2

Exercise 13.2

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.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q1.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q1.2

Question 2.
Draw a quadrilateral ABCD with AB = 6cm, BC = 4cm, CD = 4 cm and ∠ ABC = ∠ BCD = 90°
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q2.1

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.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q3.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q3.2

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.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q4.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q4.2

Question 5.
Construct a trapezium ABCD in which AD || BC, AB = CD = 3 cm, BC = 5.2cm and AD = 4 cm
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q5.1

Question 6.
Construct a trapezium ABCD in which AD || BC, ∠B= 60°, AB = 5 cm. BC = 6.2 cm and CD = 4.8 cm.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q6.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q6.2

Question 7.
Using ruler and compasses only, construct a parallelogram ABCD with AB = 5.1 cm, BC = 7 cm and ∠ABC = 75°.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q7.1

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.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q8.1

Question 9.
Using ruler and compasses, construct a parallelogram ABCD give that AB = 4 cm, AC = 10 cm, BD = 6 cm. Measure BC.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q9.1

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.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q10.1

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.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q11.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q11.2

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.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q12.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q12.2

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.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q13.1

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.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q14.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q14.2

Question 15.
Using ruler and compasses, construct a rectangle ABCD with AB = 5cm and AD = 3 cm.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q15.1

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°.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q16.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q16.2

Question 17.
Using ruler and compasses only, construct a square having a diagonal of length 5cm. Measure its sides correct to the nearest millimeter.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q17.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q17.2

Question 18.
Using ruler and compasses only construct A rhombus ABCD given that AB 5cm, AC = 6cm measure ∠BAD.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q18.1

Question 19.
Using ruler and compasses only, construct rhombus ABCD with sides of length 4cm and diagonal AC of length 5 cm. Measure ∠ABC.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q19.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q19.2

Question 20.
Construct a rhombus PQRS whose diagonals PR and QS are 8cip and 6cm respectively.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q20.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q20.2

Question 21.
Construct a rhombus ABCD of side 4.6 cm and ∠BCD = 135°, by using ruler and compasses only.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q21.1

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.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q22.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q22.2

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.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q23.1

Question 24.
Construct a regular hexagon of side 2.5 cm.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q24.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q24.2

Multiple Choice Questions

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°
Solution:
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°
Solution:
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°
Solution:
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°
Solution:
In a rectangle a diagonal is inclined to one side of the rectangle is 25°
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures mul Q4.1

Question 5.
ABCD is a rhombus such that ∠ACB = 40°. Then ∠ADB is
(a) 40°
(b) 45°
(c) 50°
(d) 60°
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures mul Q5.1

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°
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures mul Q6.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures mul Q6.2

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
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures mul Q7.1

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

Chapter Test

Question P.Q.
The interior angles of a polygon add upto 4320°. How many sides does the polygon have ?
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures ch Qp1.1

Question P.Q.
If the ratio of an interior angle to the exterior angle of a regular polygon is 5:1, find the number of sides.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures ch Qp1.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures ch Q1.3

Question P.Q.
In a pentagon ABCDE, BC || ED and ∠B: ∠A : ∠E =3:4:5. Find ∠A.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures ch Q3.1

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.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures p.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures p.2

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.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures p.3

Question 3.
Prove that the quadrilateral obtained by joining the mid-points of an isosceles trapezium is a rhombus.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 p.4
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures p.5

Question 4.
Find the size of each lettered angle in the Following Figures.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 4.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 4.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 4.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 4.4
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 4.5

Question 5.
Find the size of each lettered angle in the following figures :
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 5.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 5.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 5.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 5.4
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 5.5

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.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 6.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 6.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 6.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 6.4

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.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 7.1

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.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 8.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 8.2

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