Question

Construct an equilateral A ABC in which each side is congruent to given XY and
write the steps of construction.
X
Y​

Answer 1

Answer:

(1) 5.3 cm

Steps of construction:

1. Draw line segment AB = 5.3 cm.

2. With A as centre and radius more than half of AB, mark two arcs, one above and other below the line AB.

3. With B as centre and same radius, draw two arcs cutting the previous drawn arcs and name the point of intersection as X and Y.

4. Join XY and name the point where this line cuts AB as point P.

XY is the perpendicular bisector of AB.

(2) 6.7 cm

Steps of construction:

1. Draw line segment CD = 6.7 cm.

2. With C as centre and radius more than half of CD, mark two arcs, one above and other below the line CD.

3. With D as centre and same radius, draw two arcs cutting the previous drawn arcs and name the point of intersection as A and B.

4. Join AB and name the point where this line cuts CD as point Q.

AB is the perpendicular bisector of CD.

(3) 3.8 cm

Steps of construction:

1. Draw line segment XY = 3.8 cm.

2. With X as centre and radius more than half of XY, mark two arcs, one above and other below the line XY.

3. With Y as centre and same radius, draw two arcs cutting the previous drawn arcs and name the point of intersection as A and B.

4. Join AB and name the point where this line cuts XY as point R.

AB is the perpendicular bisector of XY.