Maharashtra Board Class 7 Maths Solutions Chapter 1 Geometrical Constructions Practice Set 1

Maharashtra State Board Class 7 Maths Solutions Chapter 1 Geometrical Constructions Practice Set 1

Question 1.
Draw line segments of the lengths given below and draw their perpendicular bisectors:
i. 5.3 cm
ii. 6.7 cm
iii. 3.8 cm
Solution:
i.
Maharashtra Board Class 7 Maths Solutions Chapter 1 Geometrical Constructions Practice Set 1 1
Line AB is the perpendicular bisector of seg PQ.

ii.
Maharashtra Board Class 7 Maths Solutions Chapter 1 Geometrical Constructions Practice Set 1 2
Line UV is the perpendicular bisector of seg ST.

iii.
Maharashtra Board Class 7 Maths Solutions Chapter 1 Geometrical Constructions Practice Set 1 3
Line ST is the perpendicular bisector of seg LM.

Question 2.
Draw angles of the measures given below and draw their bisectors:
i. 105°
ii. 55°
iii. 90°
Solution:
i. 105°
Maharashtra Board Class 7 Maths Solutions Chapter 1 Geometrical Constructions Practice Set 1 4

ii. 55°
Maharashtra Board Class 7 Maths Solutions Chapter 1 Geometrical Constructions Practice Set 1 5

iii. 90°
Maharashtra Board Class 7 Maths Solutions Chapter 1 Geometrical Constructions Practice Set 1 6

Question 3.
Draw, an obtuse-angled triangle and a right-angled triangle. Find the points of concurrence of the angle bisectors of each triangle. Where do the points of concurrence lie?
Solution:
Maharashtra Board Class 7 Maths Solutions Chapter 1 Geometrical Constructions Practice Set 1 7
The points of concurrence of the angle bisectors of both the triangles lie in the interior of the triangles.

Question 4.
Draw a right-angled triangle. Draw the perpendicular bisectors of its sides. Where does the point of concurrence lie?
Solution:
Maharashtra Board Class 7 Maths Solutions Chapter 1 Geometrical Constructions Practice Set 1 8
The point of concurrence of the perpendicular bisectors of the sides of the right angled triangle lies on the hypotenuse.

Question 5.
Maithili, Shaila and Ajay live in three different places in the city. A toy shop is equidistant from the three houses. Which geometrical construction should be used to represent this? Explain your answer.
Solution:
Since, Maithili, Shaila and Ajay live in three different places, lines joining their houses will form a triangle.
The position of the toy shop which is equidistant from three houses can be found out by drawing the perpendicular bisector of the sides of the triangle joining the three houses.
The shop will be at the point of concurrence of the perpendicular bisectors.

Maharashtra Board Class 7 Maths Chapter 1 Geometrical Constructions Practice Set 1 Intext Questions and Activities

Question 1.
Draw a line segment PS of length 4cm and draw its perpendicular bisector. (Textbook pg. no. 1)

  1. How will your verify that CD is the perpendicular bisector? m∠CMS = __°
  2. Is l(PM) = l(SM)?

Solution:
Maharashtra Board Class 7 Maths Solutions Chapter 1 Geometrical Constructions Practice Set 1 9

  1. Here, m∠CMS = 90°
  2. Also, l(PM) = l(SM) = 2cm
    ∴ line CD is the perpendicular bisector of seg PS.

Maharashtra Board Class 7 Maths Solutions

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