Practical Geometry Class-7 ML Aggarwal ICSE Maths

Practical Geometry Class-7 ML Aggarwal ICSE Mathematics Solutions Chapter-13. We provide step by step Solutions of Exercise / lesson-13 Practical Geometry ICSE Class-7th  ML  Aggarwal Maths.

Our Solutions contain all type Questions with Exe-13  Objective Type Questions ( HOTS) and Check Your Progress to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-7 Mathematics.

Practical Geometry Class-7 ML Aggarwal ICSE Mathematics Solutions Chapter-13


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Exercise 13

Objective Type Questions, 

HOTS

Check Your Progress

 


Exe -13, Practical Geometry Class-7 ML Aggarwal ICSE Mathematics Solutions

Question 1.
Draw a line, say l, take a point P outside it. Through P, draw a line parallel to l using ruler and compasses only.

Answer

Steps of construction:

  1. Draw a line l and take a point P outside it.
  2. Take another point Q on the line l and join PQ.
  3. Construct at P equal to ∠PQR.
    This is the required line which is parallel to l.
    ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13 Q1

Question 2.
Draw a line l. Draw a perpendicular to l at any point on l. On this perpendicular choose a point A, 3.5 cm away from line l. Through A, draw a line m parallel to l.

Answer

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Steps of construction:

  1. Draw a line l and take a point P on it.
  2. At P draw a ray PQ making an angle of 90°.
    PQ is the required perpendicular on the line l at point P.
    ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13 Q2

Question 3.
Let l be a line and P be a point not on l. Through P, draw a line m parallel to l. Now join P to any point Q on l. Choose any other point R on m. Through R, draw a line parallel to PQ. If this line meets l at S, then what shape do the two sets of parallel lines inclose?

Answer

Steps of construction :

  1. P is a line and P is a point not on the line l.
  2. Take point A on it and join PA.
  3. On P, draw an angle equal to ∠PAl and draw a line m which is parallel to l.
  4. Take a point Q and join PQ. From a point R on m,
    draw a line parallel to PQ which meets l at S.
    We see that PQSR is a ||gm.
    ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13 Q3

Question 4.
Construct a triangle ABC, given that
(i) AB = 5 cm, BC = 6 cm and AC = 7 cm
(ii) AB = 4.5 cm, BC = 5 cm and AC = 6 cm.

Answer

(i) Steps of construction :

  1. Draw a line segment BC = 6 cm.
  2. With centre B and radius 5 cm and with centre C and radius 7 cm,
    draw arcs which intersect each other at A.
  3. Join AB and AC.
    ∆ABC is the required triangle.
    ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13 Q4

(ii) Steps of construction :

  1. Draw a line segment BC 5 cm.
  2. With centre B and radius 4.5 cm and with centre C and radius 6 cm,
    draw arcs which intersect each other at A.
  3. Join AB and AC.
    ∆ABC is the required triangle.
    ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13 Q4.1

Question 5.
Construct a triangle PQR given that PQ = 5.4 cm, QR = PR = 4.7 cm. Name the triangle.

Answer

Steps of construction :

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  1. Draw a line segment PQ = 5.4 cm.
  2. With centre P and radius 4.7 cm and with centre Q and radius 4.7 cm,
    draw two arcs intersecting each other at R.
  3. Join RP and RQ.
    PQR is the required triangle which is an isosceles triangle.
    ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13 Q5

Question 6.
Construct a triangle LMN such that the length of each side is 5.3 cm. Name the triangle.

Answer

Steps of construction :

  1. Draw a line segment MN = 5.4 cm.
  2. With centre M and N and radius 5.4 cm,
    draw two arcs intersecting each other at L.
    ∆LMN is the required triangle which is an equilateral triangle.
    ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13 Q6

Question 7.
Construct a triangle ABC such that AB = 2.5 cm, BC = 6 cm and AC = 6.5 cm. Measure ∠ABC and name the triangle.

Answer

Steps of construction :

  1. Draw a line segment BC = 6 cm.
  2. With centre B and radius 2.5 cm and with centre C and radius 6.5 cm,
    draw two arcs intersecting each other at A.
  3. Join AB and AC.
    ∆ABG is the required triangle.
    On measuring ∠ABC it is equal to 90°.
    Therefore, ∆ABC is a right angled triangle.
    ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13 Q7

Question 8.
Construct a triangle PQR, given that PQ = 3 cm, QR = 5.5 cm and ∠PQR = 60°.

Answer

Steps of construction :

  1. Draw a line segment QR = 5.5 cm.
  2. At B, draw a ray BX making an angle of 60°
    and cut off PQ = 3 cm.
  3. Join PR.
    ∆PQR is the required triangle.
    ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13 Q8

Question 9.
Construct ∆DEF such that DE = 5 cm, DF = 3 cm and m∠EDF = 90°.

Answer

Steps of construction :

  1. Draw a line segment DE = 5 cm.
  2. At D, draw a ray DX making an angle of 90°
    and cut off DF = 3 cm.
  3. Join FE.
    ∆DEF is the required triangle.
    ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13 Q9

Question 10.
Construct an isosceles triangle in which the length of each of its equal sides is 6.5 cm and the angle between them is 110°. Measure base angles.

Answer

Steps of construction:

  1. Draw a line segment AB = 6.5 cm.
  2. At A, draw a ray AX making an angle of 110° and cut off AC = 6.5 cm.
  3. Join BC.
    ∆ABC is the required triangle.
    On measuring its base angles ∠B and ∠C, these are 35° each.
    ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13 Q10

Question 11.
Construct triangle XYZ if it is given that XY = 6 cm, ∠X = 30° and ∠Y = 100°.

Answer

Steps of construction :

  1. Draw a line segment XY = 6 cm.
  2. At X, draw a ray XA making an angle of 30° and at Y
    draw a ray YB making an angle of 100°
    which intersect each other at X.
    ∠XYZ is the required triangle.
    ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13 Q11

Question 12.
Construct a triangle PQR given that PQ = 4.9 cm, ∠P = 45° and ∠Q = 60°. Measure ∠R.

Answer

Steps of construction :

  1. Draw a line segment PQ = 4.9 cm.
  2. AP, draw a ray PX making are the angle of 45° and at Q,
    draw a ray QY making an angle of 60°
    which intersect it each other at R.
    ∆PQR is the required triangle.
    ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13 Q12

Question 13.
Construct a triangle ABC such that AB = 4.1 cm, ∠B = 90° and hypotenuse AC = 5.2 cm.

Answer

Steps of construction:

  1. Draw a line segment AB = 4.1 cm.
  2. AB, draw a ray BX making an angle of 90°.
  3. With centre A and radius 5.2 cm,
    draw an arc which intersects BX at C.
  4. Join AC.
    ∆ABC is the required triangle.
    ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13 Q13

Question 14.
Construct a right-angled triangle whose hypotenuse is 6 cm long and one of the legs is 4 cm long.

Answer

Steps of construction :

  1. Draw a line segment BC = 4 cm.
  2. At B, draw a ray BX making an angle of 90°.
  3. With centre C and radius 6 cm
    draw an arc which intersects BX at A.
  4. Join AC.
    ∆ABC is the required triangle.
    ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 13 Practical Geometry Ex 13 Q14

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