Class 07 ACTIVITY3 - LINES AND ANGLES

 ACTIVITY3 - LINES AND ANGLES

Objective: 

To verify that if two parallel lines are cut by a transversal, then each pair of interior angles on the same side of the transversal are supplementary by paper cutting and pasting

Materials Required: 

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

Procedure:

1. cutting On a white sheet of paper, draw two parallel lines AB and CD and a transversal EF cutting them at P and Q resp., Mark a point O on PQ. 

2. Cut the angular regions ∠OQC, ∠ OQD ∠ OPA and ∠ OPB.

3. Draw a line segment and take a point X on it. Paste the angular cut out OQD such that Q coincides with X and QD falls along the Straight line.

Now, paste the angular cut out OPB such that P coincides with X and PO falls along QO.

4. Draw another line segment and take a point Y on it. Paste the angular cut out OQC such that Q coincides with Y  and QC falls along the straight line. Now, paste the angular cut out OPA such that P coincides with Y and PO falls along QO.

Observations:

In figure 1, AB || CD and EF is a transversal.

So, (∠ APO, ∠ CQO) and (∠ BPO, ∠ DRO) are two pairs of interior angles on the same side of the transversal.

2. In figure 3, BD is a straight line. So, ∠ BXD = 180 °or

 ∠ BPO + ∠ DRO = 180 °

3. In figure 4, AC is a straight line.

So, ∠ AYC = 180 °or ∠ APO + ∠ CQO = 180 °

Conclusion: 

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

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.

Class 07 ACTIVITY1 - LINES AND ANGLES

 ACTIVITY1 - LINES AND ANGLES

Objective: 

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

Materials Required: 

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

Procedure:

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

2. Cut the figure along the dotted lines to get four angular cut outs as shown below.

3. Paste the angular cutout ∠ DQO over ∠ BPE such that Q coincides with P and QD falls along PB.

4. Similarly, paste the angular cut outs ∠DQF,   ∠ CQF and ∠ CQO over ∠ BPO, ∠ APO and ∠ APE resp., such that in each case Q coincides with P and one arm of each angle falls along one arm of the corresponding angle.

Observations:

In figure1, AB ∥ CD and EF is Transversal. So, (∠ EPB, ∠ DQO), (∠ BPO, ∠ DQF), (∠ APE, ∠CQP) and (∠ APQ, ∠ CQF ) are four pairs of corresponding angles.

2. In figure, we see that if vertex Q of ∠ DQO coincides with the vertex P of ∠ BPE and QD falls along PB, then QO falls along PE, i.e., DQO completely overlaps BPE. So, ∠ DQO = ∠ BPE.

3. Similarly, in fig, we see that ∠ DQF, ∠ CQF and ∠ CQO completely overlap ∠ BPO, ∠ APO and ∠ APE resp.,

So, ∠ DQF = ∠ BPO, ∠ CQF = ∠ APO and ∠ CQO = ∠ APE

Conclusion : 

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

Do yourself: 

Verify the above property by drawing a pair of parallel lines which are 5 cm apart.

Class 07 Fun Activity – Algebraic Expression CROSS NUMBER PUZZLE

 Fun Activity – Algebraic Expression
CROSS NUMBER PUZZLE

Find the root of the given equations and complete the following cross number puzzle

Fun Activity – Algebraic Expression -  solution

CROSS NUMBER PUZZLE

Find the root of the given equations and complete the following cross number puzzle

CROSS NUMBER PUZZLE

Find the root of the given equations and complete the following cross number puzzle