7th Standard Maths - Exercise 5.3 Solutions

7th Standard Mathematics — Chapter 5: Geometry

Exercise 5.3 Solutions (Construction of Perpendicular Bisector)

1. Draw a line segment of given length and construct a perpendicular bisector to each line segment using scale and compass.

(a) Length = 8 cm

Steps of Construction:

Draw a line segment AB = 8 cm using a ruler.
With center A and radius more than half of AB (e.g., 5 cm), draw two arcs—one above and one below AB.
With center B and the same radius, draw two arcs intersecting the previous arcs at points C and D.
Join CD intersecting AB at point O.
Line CD is the required perpendicular bisector of AB, where AO = OB = 4 cm and ∠AOC = 90°.

Steps of Construction:

Draw a line segment AB = 7 cm.
With center A and radius > 3.5 cm (e.g., 4.5 cm), draw two arcs above and below AB.
With center B and same radius, draw arcs cutting the first arcs at C and D.
Join CD cutting AB at O.
CD is the perpendicular bisector of AB (AO = OB = 3.5 cm).

Steps of Construction:

Steps of Construction:

Draw line segment AB = 10.4 cm using scale.
With center A and radius > 5.2 cm (e.g., 6.5 cm), draw two arcs above and below AB.
With center B and same radius, draw arcs cutting the previous arcs at C and D.
Join CD cutting AB at O.
CD is the perpendicular bisector of AB (AO = OB = 5.2 cm).

Note: 58 mm = 5.8 cm (since 10 mm = 1 cm).

Steps of Construction: