Class 07 ACTIVITY 4 - TRIANGLES

 ACTIVITY 4 - TRIANGLES

Objective: 

To medians get the pass medians through of a a common triangle by point paper. folding. Also, to verify that in a triangle medians pass through a common point.

Materials Required: 

Tracing paper, colour pencils, geometry box, etc.

Procedure:

1. On a. tracing paper, trace the following triangles. Cut out each triangle from the tracing paper. Note that triangle (a) is an equilateral triangle, triangle (b) is isosceles as well as right angled triangle and  triangle(c) is as a scalene triangle. We can also say that triangle (a) is an acute angled triangle, (b) is right angled triangle, (c) is an obtuse angled triangle.

2. Fold each triangular cut out such that the vertex Q coincides with the vertex R.

3. Unfold each tracing paper. In each case mark the point of intersection of QR and the crease as X. Draw PX as dotted line.

4. Now, fold each triangular cut out such that the vertex P and R coincide.

5. Unfold each tracing paper. In each case mark the point of intersection of PR and the crease P as Y. Draw QY as a dotted line.

6. Finally fold each triangular cutout such that the vertex P coincides with the vertex Q.

7. Unfold each tracing paper. In each case mark the point of intersection of PQ and the crease as Z. Draw RZ as a dotted line. 

Observations :

In figure 3, X is the mid point of QR. So PX is a median of  each triangle.

2. Similarly in figures 5 and 7,  Y and Z are mid points PR and PQ respectively. So QY and RZ are medians of ∆PQR in each case.

3. Also  in figure 7, we see that in each case all the three medians pass through a common point O.

Conclusion

A triangle has three medians.

2. All the three medians of a triangle pass through a common point. This point is called the centroid of the angle.

Do Yourself: 

Draw an acute angled, a right angled and an obtuse angled triangle. By paper folding, verify that in each case the three medians are  concurrent.

Class 07 ACTIVITY 3 - TRIANGLES

 ACTIVITY 3 - TRIANGLES

Objective: 

To verify that an exterior angle of a triangle is equal to the sum of the two interior opposite angles by paper cutting and pasting.

Materials Required: 

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

Procedure:

On a white sheet of paper, draw a triangle ABC. Produce its side BC to D as shown in the figure. Using Colour pencils, mark its angles as shown.

2. Using a pair of scissors, cut out the two marked angular regions as shown below.

3. Paste the angular cutouts A and B over exterior angle C such that vertices A, B and C coincide as shown.

Observations:

In figure, ∠ACD is an exterior angle of ∆ABC and  ∠ A and ∠ B are its two interior opposite angles

2. In figure, we see that the angular cutouts neither overlap nor leave any gap between them. In other words, the angular cut outs A and B completely cover exterior angle C.

or ∠ A + ∠ B = exterior angle C. or ∠ A + ∠ B = ∠ ACD

Conclusion: 

From the above activity, we can say that an exterior angle of a triangle is equal to the sum of the two interior opposite angles.

Do Yourself: 

Copy each of the following triangles. In each case verify that an exterior angle of a triangle is equal to the sum of two interior opposite angles.

Class 07 ACTIVITY 2 - TRIANGLES

 ACTIVITY 2 - TRIANGLES

Objective: 

To verify the angle sum property of a triangle by paper folding.

Materials Required: 

White sheets of paper, tracing paper, geometry box, a pair of scissors, etc.

Procedure:

On a white sheet of paper, draw a fairly large triangle ABC. Using scissors, cut it out. Mark A, B and C on both sides of the cutout.

2. Fold the side BC of ∆ABC such that the folding line passes through A.

3. Unfold it and draw a line along the crease. This line cuts BC at D.

4. Fold the vertices (three corners) of ∆ABC such that A, B and C meet at D.

Observations: 

In figure 4, we see that the angles A, B and C form a straight angle 

i.e., ∠A + ∠ B + ∠ C = 180°

Conclusion: 

From the above activity, it is verified that the sum of the angles of a triangle is 180 °

Do Yourself:  

Draw an acute angled triangle, a right angled triangle. By paper folding, verify the angle sum property in each case.

Class 07 ACTIVITY - Triangles

 ACTIVITY - Triangles

Objective: 

To verify that the sum of all interior angles of a triangle is 180 °, by papercutting and pasting.

Materials Required: 

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

Procedure:

On a white sheet of paper, draw a triangle ABC. Using colour pencils mark its angles as shown.

2. Using a pair of scissors, cut out the three angular regions.

3. Draw a line segment XY and mark a point on it.

4. Paste the three angular cut outs so that the vertex of each falls at O as shown in the figure.

Observations:

In figure 4, we see that the angular cutouts neither overlap nor leave any gap between them. But, XOY is a straight angle So, ∠A + ∠ B + ∠C = 180 ° Or sum of the angles of a triangle is 180 °.

Conclusion: 

From the above activity, it is verified that the sum of all interior angles of a triangle is 180 °

Do Yourself: 

Draw an acute angled triangle, a right triangle and an obtuse angled triangle. By paper cutting and pasting, verify the above property for each triangle.