TO DRAW PARALLEL LINE -- To draw a line through a point and parallel to a given straight line

A) To draw a line through a given point, parallel to a given straight line

1. Let AB be the given line and P be the given point at a distance.

2. With centre P any convenient radius, draw an arc CD cutting AB at E.

3. With the same radius, from point E as centre draw an arc cutting AB at F.

4. Point E as centre and radius equals to FP, draw an arc cutting CD at Q.

5. Draw a line connecting PQ, This is the required line parallel to AB.

 

B) To draw a line parallel to, and at a given distance from a straight line

1. Let AB be the given line and R is the given radius.

2. Mark points P and Q on line AB, as far apart as convenient.

3. By taking R as radius draw an arc C from given point P.

4. with same radius draw another arc D from point Q.

5. Draw the line CD, just touching the two arc's, now this becomes the parallel line to the given line AB.

TO CONSTRUCT SQARES

A) By using Ruler and set square:

 1. Using a ruler or T-Square, draw a line segment AB corresponding to the length of one side of the square.

2. Place the set square at one end of the line segment (i.e., A) and draw a perpendicular line that is longer than the side of the square.

3. Using the ruler, mark a point on this line that corresponds to the length of the side of the square.

4. Place the set square at another end of the line segment (i.e., B) and draw a perpendicular line that is longer than the side of the square.

5. Using the ruler, mark a point on this line that corresponds to the length of the side of the square.

6. Using the ruler, connect the two marks made in steps 3 and 5 to form the square.

B) By using T-square and set square:

1. Using a ruler or T-Square, draw a line segment AB corresponding to the length of one side.

2. At A and B draw verticals AE and BF

3.  From point A draw a line  inclined at 45 to AB, Cutting line BF at C.

4.  From point B draw a line  inclined at 45 to AB, Cutting line AE at D.

5. Draw a line connecting C and D.

6. Then ABCD is the required square.

C) By using compass:

1. Draw a line segment AB corresponding to the length of one side.

2. At A, draw a line AE perpendicular to AB.

3. With centre A, and radius AB, draw an arc cutting AE a D.

4. With centre B, and radius AB, draw an arc.

5. With centre D, and same radius draw an arc cutting previously draw arc from B.

6. Mark the intersecting point as C.

7. Draw lines C with B, C with D.

8. Then ABCD is the required square.

Construct an Equilateral triangle, given the length of side, using set squares

1. Draw a line using a scale of any length as AB.

2. With 30°-60° set square draw a line through A, making an angle 60° with AB.

3. Similarly , through B, draw a line making same angle with AB intersecting previously drawn line at C. 

4. Then ABC is the required triangle.

To draw Tangent to a given circle at any point on it

 1) With centre ‘O’, draw a circle of any radius, and mark a point ‘P’ on it.

2) Draw a line joining O and P.

3)  Extend this line OP to Q so that OP=PQ.

4) Take any convenient radius and O as centre draw an arc as shown below,

5)  By taking same radius and Q as centre draw another arc cutting previously drawn arc as shown

6) Draw a line through P and R. Then this line is the required Tangent.

Question

1) Construct a tangent at any point P on a circle of radius 3 cm.

2) Draw a circle of radius 4 cm and construct a tangent at any point on the circle.

 

TO FIND CENTRE OF AN ARC

Method 1:

1. Draw an Arc AB

2. Draw any two chords on arc as CD, EF

3. Draw Bisector to CD, 

4. Draw Bisector to EF, 

5. Extend these bisectors until they meet at a point.

6. Mark this point as 'O'.

7. This point 'O' is the centre of the arc.

Trisecting an angle

          An angle Trisector divides an angle into three equal angles. If the angle is 'θ', the three angles made after trisecting will be 'θ/3'.

Problem: To Trisect a given Angle ABC

1. Let us consider some angle ∠ABC, B as vortex,

2. Take some length in compass and place your compass on the vertex of the angle, here on point B. Draw an arc that crosses both sides of the angle, lines AB and BC. Mark those points as D,E as shown,

3. Connect D and E with scale, 

4. Mark centre point of DE line (or Draw an angular bisector) mark it as 'T', with TD or TE length draw an arc as 'T' as centre.

5. With the same length draw two arcs from point D and E on previously drawn arc.

6. Mark the point of intersections as F, G.

7. Connect FB and GB points with scale, these will form an Angular Trisector of previously given angle.