PART - 2 CH : 6 Constructions and Tilings — MATHS STD 7 — Question

The following are the given angles:


We shall make a copy of each of the above angles one by one.
Angle (i): Draw a line A’B’ along the direction of the line AB.
With centre at B and B’, draw arcs of equal radius.
Let the arc intersect AB and BC at M and N, respectively.
Let the arc intersect A’B’ at M.
Measure MN using a compass.
Transfer this length on the arc from M’ to get M’N’ = MN.
Join B’ and N’.
∠A’B’C’ is the required angle.
Angle (ii): Draw a line D’E’ along the direction of the line DE.
With centres at E and E’, draw arcs of equal radius.
Let the arc intersect DE and EE at O and P, respectively.
Let the arc intersect D’E’ at O’.
Measure OP using a compass.
Transfer this length on the arc from O’ to get O’P’ = OP.
Join E’ and P’.

∠D’E’F’ is the required angle.
Angie (iii): Draw a line G’H’ along the direction of the line GH.
With centres at H and H’, draw arcs of equal radius.
Let the arc intersect GH and HI at Q and R, respectively.

Let the arc intersect G’H’ and at Q’.
Measure QR using a compass.
Transfer this length on the arc from Q’ to get Q’R’ = QR.
Join H’ and R’.
∠G’H’I’ is the required angle.
Angle (iv): Draw a line J’K’ along the direction of the line JK.
With centres at K and K’, draw arcs of equal radius.
Let the arc intersect JK and KL at S and T, respectively.
Let the arc intersect J’K’ at S’.
Measure ST using a compass.
Transfer this length on the arc from S’ to get S’T’ = ST.

Join K’ and T.
∠J’K’L’ is the required angle.