Mathematics
Can you construct a square in the centre of a rectangle as shown in the adjoining figure?
Answer
Yes, we can construct a square in the centre of a rectangle.
Steps:
Draw a line segment AB = 10 cm using a ruler.
At A, construct a perpendicular AX to AB. From AX, cut off AD = 4 cm.
At B, construct a perpendicular BY to AB. From BY, cut off BC = 4 cm.
Join CD. Then ABCD is a rectangle with AB = 10 cm and BC = 4 cm.
Find the mid-point M of AB by drawing its perpendicular bisector. So AM = MB = 5 cm.
From M, cut off MP = 2 cm along MA and MQ = 2 cm along MB. So PQ = MP + MQ = 4 cm.
At P, draw a line perpendicular to AB cutting CD at point S.
At Q, draw a line perpendicular to AB cutting CD at point R.
Then PQRS is a square of side 4 cm constructed at the centre of the rectangle ABCD.
Hence, the square is constructed in the centre of the rectangle.
Related Questions
Construct a toy house tent as given in the adjoining figure.
Construct a square of side 5 cm, with a small circle of radius 1 cm inside it, having the same centre as the square.
Fill in the blanks:
(i) A ruler is used to draw line ….. and to measure their …..
(ii) A divider is used to compare …..
(iii) A compass is used to draw circles or arcs of …..
(iv) A protractor is used to draw and measure …..
(v) The set squares are two triangular pieces having angles of …….. and …..
(vi) To bisect a line segment of length 7 cm, the opening of the compass should be more than …..
(vii) The perpendicular bisector of a line segment is also its line of …..
State whether the following statements are true (T) or false (F):
(i) There is only one set square in a geometry box.
(ii) An angle can be copied with the help of a ruler and compass.
(iii) The perpendicular bisector of a line segment can be drawn by paper folding.
(iv) A perpendicular to a line from a given point not on it can be drawn by paper folding.
(v) A 45° - 45° - 90° set square and a protractor have the same number of line(s) of symmetry.