Std 6 th Mathematics- 17. Geometrical Constructions

Question 1:

Draw line l . Take any point P on the line. Using a set square, draw a line perpendicular to line l at the point P.

Answer 1:

Steps of constructions:
1. Draw line l. Take point P anywhere on the line.
2. Place the set square on the line in such a way that the vertex of its right angle is at point P and one arm of the right angle falls on line l.
3. Draw a line PQ along the other arm of the right angle of the set square.
4. The line PQ is perpendicular to the line l at P.

Question 2:

Draw a line AB. Using a compass, draw a line perpendicular to AB at the point B.

Answer 2:

Steps of construction:
1. Draw line AB.
2. Place the compass point on point B. Draw two arcs on either side of point B to cut the line AB at equal distances from B. Name the points of intersection M and N respectively.
3. Place the compass point at M and, taking a convenient distance greater than half the length of MN, draw an arc on one side of the line.
4. Place the compass point at N and using the same distance, draw another arc to intersect the first one at P.
5. Draw a line passing through points B and P.
6. The line BP is perpendicular to line AB at B.

Question 3:

Draw line CD. Take any point M on the line. Using a protractor, draw a line perpendicular to line CD at the point M.

Answer 3:

Steps of construction:
1. Draw line CD. Take point M anywhere on the line.
2. In order to draw a perpendicular through M, place the centre of the protractor on point M.
3. Mark a point N at the 90° mark on the protractor.
4. Draw a line passing through points M and N.
5. The line MN is perpendicular to line CD at M.

Question 1:

Draw line l . Take point P anywhere outside the line. Using a set square, draw a line PQ perpendicular to line l .

Answer 1:

Steps of construction:
1. Draw line l. Take point Q anywhere outside l.
2. Place one of the arms of the right angle of a set square along the line l.
3. Slide the set square along the line in such a way that the other arm of its right angle touches point P.
4. Draw a line along this side, passing through point Q. Name the line PQ.

Question 2:

Draw line AB. Take point M anywhere outside the line. Using a compass and ruler, draw a line MN perpendicular to line AB.

Answer 2:

Steps of construction:
1. Draw line AB. Take any point M outside the line.
2. Placing the compass point at point M and using any convenient distance, draw arcs to cut the line AB at two points P and Q.
3. Place the compass point at P and taking a distance greater than half of PQ, draw an arc on the lower side of line AB.
4. Place the compass point at Q and using the same distance, draw an arc to cut the previous arc at N.
5. Draw the line MN.
6. Line MN is perpendicular to line PQ. 

Question 3:

Draw a line segment AB of length 5.5 cm. Bisect it using a compass and ruler.

Answer 3:

Steps of constructions:
1. Draw seg AB of 5.5 cm.
2. Place the compass point at A and taking a distance greater than half the length of seg AB, draw two arcs, one below and one above seg AB.
3. Place the compass point at B and using the same distance draw  arcs to intersect the previous arcs at P and Q.
4. Draw line PQ.

Question 4:

Take a point R on line XY. Draw a line perpendicular to XY at R, using a set square.

Answer 4:

 
Steps of constructions:
1. Draw line XY. Take point R anywhere on the line.
2. Place the set square on the line in such a way that the vertex of its right angle is at point R and one arm of the right angle falls on line XY.
3. Draw a line PQ along the other arm of the right angle of the set square.
4. The line RS is perpendicular to the line XY at R.