# GEOMETRICAL FIGURES

### Draw a Square of side 50 mm.

- Draw a line AB 50 mm long.

- ‘A’ as centre, draw an arc of convenient radius ‘r’ touching the line AB at ‘P’ as shown in Figure.

- ‘P’ as centre and radius ‘r’ draw another arc cutting the earlier drawn arc at `Q’.

- ‘Q’ as centre and radius ‘r’, draw another arc cutting at ‘R’.

- Bisect QR at S and extend.

- Mark 50 mm on AS extended line. AD = 50 mm.

- From points B and D, draw parallels to AD and AB and complete the square ABCD.

### Draw a square of side 60 mm using 45° setsquare and compass.

- Draw a horizontal line AB = 60 mm long.

- From points A and B, using 45° setsquare, draw 45° lines both intersecting at ‘0’.

- Draw a circle of radius OA or OB with centre ‘0’.

- ‘A’ as centre and AB as radius, draw an arc. The arc cuts the circle at D.

- Similarly draw an arc with centre D with radius AB and get point C.

- Join AD, DC & CB and complete the square.

### Draw a square of side 60 mm long by erecting perpendicular and also using 45° set square.

- Draw line AB equal to 60 mm.

- Erect perpendicular from A and B using 60° or 45° setsquare.

- Draw 45° from A and B, cutting perpendicular lines at C and D.

- Join A,D,C and B. ABCD is required square.

### Draw Square having diagonal 60 mm

- Draw horizontal and vertical centre lines intersecting at ‘0’.

- ‘0’ as centre, draw a circle of radius 30 mm passing through centre lines at A,B,C and D.

- Join points A-B, B-C, C-D and D-A. ABCD is the required square, whose diagonal is 60 mm.

### Draw a Rectangle with sides 75 mm and 45 mm using setsquare and compass.

- Draw the side AB equal to 75 mm.

- Erect perpendiculars at A and B.

- Mark off a height 45 from A and B, at D and C.

- Join C and D to complete the rectangle.

### Draw a Rectangle with Diagonal 60 mm and one side 20 mm.

1st method (Fig a)

- Draw a line AB 60 mm.

- Draw a circle with AB as its diameter.

- ‘A’ as centre, draw an arc of R20, cutting the circle at D.

- Join AD and BD.

- Draw AC parallel to DB.

- Join BC and complete the rectangle.

2nd method (Fig b)

- Draw a line AD = 20 mm long.

- Draw perpendiculars from A and D upwards.

- A and D as centres, draw arcs of 60 mm radius cutting at B and C.

- Join BC.

- ADBC is the required rectangle of side 20 mm and diagonal 60 mm.

### Draw a parallelogram with sides 75 mm and 40 mm and angle 50°.

- Draw line AB 75 mm long.

- Draw line AD equal to 40 mm and 50° angle to AB.

- D as centre, draw an arc of radius equal to AB.

- ‘B’ as centre, draw an arc of radius equal at AD, upwards such that they meet at a point ‘C’.

- ABCD is the required parallelogram.

### Draw a Parallelogram with side – 60 mm , Diagonal – 90 mm and Angle 120°.

- Draw a line AB = 60 mm.

- Draw a line from B at angle of 120° to AB.

- ‘A’ as centre with radius 90 mm, draw an arc cutting 120° line from B at C.

- `C’ as centre, radius = AB, draw an arc.

- Similarly `A’ as centre and BC as radius, draw another arc, both arcs meet at `D’.

- Join AD and DC.

- ABCD is the required parallelogram.

### Draw a parallelogram with sides 55 mm and 40 mm and vertical height of 30 mm.

- Draw the line AB 55 mm long.

- A and B as centres and radius (R) 30 mm, draw arcs above the line.

- Draw a common tangential line (parallel to base AB) to the arcs.

- A and B as centers, draw an arc of 40 mm radius cutting the line at D and C.

- ABCD is the required parallelogram.

### Draw a Rhombus with diagonals of 80 mm and 50 mm.

- Draw a line AB equal to 80 mm.

- Draw perpendicular bisector of AB, passing through 0.

- Mark OC = OD = 25 mm.

- Join the points AC, CB, BD and DA to complete the rhombus.

### Draw a tangent to a given circle of Φ 70 mm at any point `P’ on it.

- Draw a circle of φ 50 with `O’ as centre.

- Mark the given point `P’ on the circumference of the circle.

- Join OP.

- Draw a line RS perpendicular to PO through `P’.

- RS is the tangent at `P’.

### Draw an arc of given radius (R 20 mm) to touch to two straight lines (50 mm each) at right angles.

- Draw the lines AB and AC (50 mm each) at right angles.

- With `A’ as centre and given radius (R 20 mm) draw an arc to cut lines AB and AC at E and F.

- With E and F as centres and the radius given (R 20 mm), draw arcs to intersect each other at `O’.

- Use `O’ as centre and with same radius (R 20) draw a curve (arc) which will just touch the given lines AB and AC.

### Draw an arc of given radius (R 20 mm) to touch the given lines which make an acute angle between them (assume 60°).

- Draw an acute angle BAC (60°).

- Draw a horizontal parallel line EF at a distance equal to the given radius (20 mm).

- Draw another angular parallel line GH at a distance of given radius 20 mm. Both the parallel lines drawn meet at `O’.

- With `O’ as centre and `r’ as radius (20 mm) draw an arc touching both lines AB and AC.

### Draw a loop of 3 circles pattern.

- Draw any line MN and mark points A,B and C. So that AB = 20 mm and BC = 25 mm.

- With ‘A’ as centre draw concentric circles of dia 15 mm and dia 20 mm.

- With ‘B’ as centre draw concentric circles of Φ 20 mm and Φ 25 mm.

- With ‘C’ as centre draw concentric circles of Φ 25 mm and Φ 30 mm.

- Erase unwanted part of the circles to form the pattern.