Mathematics Lab Activity-06 Class IX | Lines & Angles

  Lab Activity-06 Class iX

Mathematics Lab Activities on Lines & Angles for class IX students, with complete observation tables, strictly according to the CBSE syllabus.

Chapter - 06  Lines & Angles

Activity - 06

Objective: 

To verify experimentally that if two lines intersect, then

(i) the vertically opposite angles are equal

(ii) the sum of two adjacent angles is 180º

(iii) the sum of all the four angles is 360º.

Material Required

Two transparent strips marked as AB and CD, a full protractor, a nail,cardboard, white paper, etc.

Procedure

1. Take a cardboard of a convenient size and paste a white paper on it.

2. Paste a full protractor (0° to 360º) on the cardboard, as shown in Fig. 1.

3. Mark the centre of the protractor as O.

4. Make a hole in the middle of each transparent strip containing two intersecting lines.

5. Now fix both the strips at O by putting a nail as shown in Fig. 1.

Figure 1

6. Observe the adjacent angles and the vertically opposite angles formed in different positions of the strips.

7. Compare vertically opposite angles formed by the two lines in the strips in different positions.

8. Check the relationship between the vertically opposite angles.

9. Check that the vertically opposite angles ∠AOD, ∠COB, ∠COA and ∠BOD are equal.

10. Compare the pairs of adjacent angles and check that ∠COA + ∠DOA= 180º, etc.

11. Find the sum of all the four angles formed at the point O and see that the sum is equal to 360º.

Observations

On actual measurement of angles in one position of the strips :

1. ∠AOD = 90º, ∠AOC = 90º, ∠COB = 90º, ∠BOD = 90º.

Therefore, ∠AOD = ∠COB = 90º   (vertically opposite angles are equal)

         and   ∠AOC = ∠BOD =  90º  (vertically opposite angles are equal).

2. ∠AOC + ∠AOD = 90º + 90º = 180º ...(Linear pairs of angles).

∠AOC + ∠BOC = 90º + 90º = 180º ...(Linear pairs of angles).

∠COB + ∠BOD = 90º + 90º = 180º  ...(Linear pairs of angles).

∠AOD + ∠BOD = 90º + 90º = 180º ...(Linear pairs of angles).

3. ∠AOD + ∠AOC + ∠COB + ∠BOD = 360º ... (angles formed at a point).

4. Students may revise this concept by taking some different angles other than 90º.

Result : 

With the help of this activity we prove that when two lines intersect each other then

i) Vertically opposite angles are equal.

ii) Linear pair of angles are supplementary.

iii) Sum of all angles at one point is always equal to 360º.

Applications

These properties are used in solving many geometrical problems.

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