Page 336 - Math_Genius_V1.0_C7_Flipbook

D:\Surender Prajapati\CBSE_ICSE_Book_New\CBSE\Grade-7\Math_Genius-7\Open_File\15_Chapter\15_Chapter
\ 15-Nov-2024 Surender Prajapati Proof-5 Reader’s Sign _______________________ Date __________

5. By measuring line segment BC, we find that BC = 2.5 cm.

AB = 6.2 cm

AC = 3.7 cm

l BC = 2.5 cm
A 3.7 cm C 2.5 cm B

6.2 cm
Example 2: Given AB of length 3.5 cm. Construct PR such that the length of PR is twice that of AB.
Verify it by measurement.
Solution: Steps of construction:

1. Draw AB = 3.5 cm A 3.5 cm B
2. Draw a line l and mark point P on it.

3. Place the pointer of the compass on point A and pencil point on B.
4. Without changing the measure, place the pointer of compass on the point P and
draw an arc that cuts l at Q.
5. Again place the compass at Q and without changing the measure, cut another arc
that cuts l at R.
6. Join PR. PR is the required line segment such that PR = 2AB.

PR = 2 AB

l
P 3.5 cm Q 3.5 cm R

A 3.5 cm B
By measuring, we find that PR = 7 cm which is equal to 2 × 3.5 cm, i.e., 2AB.

Example 3: Given AB of length 7.1 cm and CD of length 3.9 cm, construct a line segment XY such
that the length of XY is equal to the difference between the lengths of AB and CD. Verify it by
measurement.

Solution: Steps of construction:
1. Given AB = 7.1 cm and CD = 3.9 cm
2. Draw a line l. Mark a point X on line l.

3. Measure AB = 7.1 cm in compass.
4. Without changing the measurement, place the compass on X and draw an arc that
cuts l at Z. (XZ = 7.1 cm)

5. Now measure CD = 3.9 cm in compass and without changing the measurement,
place the compass at Z and draw an arc on the left of Z, that cuts l at Y.

Mathematics-7 334