Construction of Perpendicular from a Point Outside the Line Using a Set Square

Q. Draw a line segment of length 6cm. Construct its perpendicular bisector. Measure the two parts of the line segment.

Q.

Steps for constructing a line segment whose length is equal to the sum of the lengths of the two given line segments are:

(i) Draw two line segments AB and CD using a ruler.

(ii) Now take a line L.

(iii) PM is the required Line segment.

(iv) Using the compass a cut a line PQ equal to AB on line L.

(v) Now from Q cut a length QM equal to CD.

1. i, iii, ii, iv, v

2. i, ii, iii, iv, v

3. i, ii, iii, v, iv

4. i, ii, iv, v, iii

Q. Measure the angle between the perpendicular bisectors of two lines segments each of length 10 cm which are perpendicular to each other.

Q. Given below are the steps to draw a perpendicular to a line segment AB passing through a point C which is not on the line by using a ruler and a set square. Arrange these steps in a logical sequence to make the above mentioned construction.

1. Hold the ruler fixed. Slide the set square along one edge of the ruler till the point C touches the other arm of the set square.
2. Draw a line segment CD along the edge through C, meeting AB at D.
3. Place a ruler along the edge opposite to the right angle of the set square. Draw the line AB.
4. Place a set square on AB such that one arm of its right angle aligns along AB.

1. 1234
2. 3421
3. 4312
4. 4231

Q. Construct a rectangle whose adjacent sides are 8 cm and 3 cm.

Q. Draw a line segment AB of length 10 cm. Mark a point P on AB such that AP = 4 cm. Draw a line through P perpendicular to AB.

Q. If AB = 7.5 cm and CD = 2.5 cm, construct a segment whose length is equal to

(i) AB − CD
(ii) 2AB
(iii) 3CD
(iv) AB + CD
(v) 2AB + 3CD

Q. Write the steps of constructing perpendicular using a set-square. (3 Marks)