Class 07 ACTIVITY2 - LINES AND ANGLES

 ACTIVITY2 - LINES AND ANGLES

Objective:

 To verify that if two parallel lines are cut by a transversal, then each pair of alternate interior angles are equal by paper cutting and pasting

Materials Required : 

glue stick, White sheets of paper, colour, pencils, geometry box, a pair of scissors, etc., 

Procedure:

On a white sheet of paper, draw a pair of parallel lines AB and CD. Also, draw a transversal EF cutting them at P and Q resp., Mark a point O somewhere in the middle of PQ. Mark the angles as shown.

2 . Cut the angles ∠ OQD and ∠ OQC.

3. Paste the angular cutouts ∠ CQO and ∠ DQO over ∠BPO and ∠ APO respectively such that in each case the vertex Q coincides with vertex P and one arm of each angle falls along one arm of the corresponding angles.

Observations: 

In figure 1, AB || CD and EF is a transversal. So, (∠APO, ∠ DRO) and (∠ BPO, ∠ CQO) are two pairs of alternate interior angles.

2. In figure 3, we see that if vertex Q of ∠ CQO coincides with vertex P of ∠ BPO and arm QC falls along PB, then QO  falls along PO, i.e., ∠ CQO completely overlaps ∠ BPO.

So, ∠ CQO = ∠ BPO 

Similarly, ∠ DQO completely overlaps ∠ APO.

So, ∠ DQO = ∠ APO transversal 

Conclusion : 

From the above activity, interior, we can say that if two parallel lines are cut by a transversal, then each pair of alternate interior angles are equal.