Mathematics Lab Activity-11 Class X | Triangle

        Mathematics Lab Activity-11 Class X

Mathematics Laboratory Activities on Similarity of Triangles for class X students with complete observation tables strictly according to the CBSE syllabus.

Chapter - 06 triangle

Activity - 11

Objective

To verify Basic Proportionality Theorem (Thales theorem).

Material Required

Two wooden strips (each of size 1 cm wide and 30 cm long), cutter, adhesive, hammer, nails, bard board, white paper, pulleys, thread, scale and screw etc.

Procedure

1. Cut a piece of hardboard of a convenient size and paste a white paper on it.

2. Take two thin wooden strips with markings 1, 2, 3, ... at equal distances and fix them vertically on the two ends of the horizontal strip as shown in Fig. 1 and call them AC and BD.

3. Cut a triangular piece PQR from hardboard (thickness should be negligible) and paste coloured glazed paper on it and place it between the parallel strips AC and BD such that its base QR is parallel to the horizontal strip AB as drawn in figure 1.

Figure. 1

4. Graduate the other two sides of the triangular piece as shown in the figure.

5. Put the screws along the horizontal strip and two more screws on the top of the board at the points C and D such that A, B, D and C become four vertices of a rectangle.

6. Take a ruler (scale) and make four holes on it as shown in the figure and fix four pulleys at these holes with the help of screws.

7. Fix the scale on the board using the thread tied to nails fixed at points A, B, C and D passing through the pulleys as shown in the figure, so that the scale

slides parallel to the horizontal strip AB and can be moved up and down over the triangular piece freely.

8. Set the scale on vertical strips parallel to the base QR of △PQR, say at the points E and F. Measure the distances PE and EQ and also measure the distance PF and FR. It can be easily verified that

This verifies Basic Proportionality Theorem (Thales theorem).

9. Repeat the activity as stated above, sliding the scale up and down parallel to the base of the triangle PQR and verify the Thales theorem for different positions of the scales.

Observations & calculations

By actual measurement:

PE = 5,  PF = 5,  EQ = 7, FR = 7

     .........(1)

  ........... (2)

From (1) and (2) we get 

 

⇒ Basic Proportionality Theorem is verified.

Result

If a line is drawn parallel to one side of a triangle to intersect the other two sides at two distinct points then other two sides are divided in the same ratio.

Applications.

The theorem can be used to establish various criteria of similarity of triangles. It can also be used for constructing a polygon similar to a given polygon with a given scale factor.

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