Mathematics Lab Activity-10 Class X | Triangle

       Mathematics Lab Activity-10 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 - 10

Objective

To draw a system of similar squares, using two intersecting strips with nails.

Material Required

Two wooden strips (each of size 1 cm wide and 30 cm long), adhesive, hammer, nails.

Procedure

1. Take two wooden strips say AB and CD.

2. Join both the strips intersecting each other at right angles at the point O [see Fig. 1].

3. Fix five nails at equal distances on each of the strips (on both sides of O) and name them, say A₁, A₂, ......., A₅, B₁, B₂, ......., B₅, C₁, C₂, ......., C₅ and D₁, D₂, ......., D₅ [see Fig. 2].

Figure 1

4. Wind the thread around nails of subscript 1 (A1C1B1D1) on four ends of two strips to get a square [see Fig. 3].

5. Similarly, wind the thread around nails of same subscript on respective strips [see Fig. 3]. We get squares A1C1B1D1 , A2C2B2D2, A3C3B3D3, A4C4 B4 D4 and A5C5B5D5.

Figure 2

Figure 3

6 On each of the strips AB and CD, nails are positioned equidistant to each other, such that

A1A2 = A2A3 = A3A4 = A4A5, B1B2 = B2B3 = B3B4 = B4B5 , C1C2 = C2C3 = C3C4 = C4C5, D1D2 = D2D3 = D3D4 = D4D5

7. Now in any one quadrilateral say A4C4B4D4 [see Fig. 3]. 

          A4O = OB4 = 4 units.

Also, D4O = OC4 = 4 units,

where 1 unit = distance between two consecutive nails.

Therefore, diagonals bisect each other.

Therefore, A4C4B4D4 is a parallelogram.

Moreover, A4B4 = C4D4 = 4 × 2 = 8 units, i.e., diagonals are equal to each other.

In addition to this, A4B4 is perpendicular to C4D4 (The strips are perpendicular to each other).

Therefore, A4C4B4D4 is a square.

Similarly, we can say that A1C1B1D1, A2C2B2D2, A3C3B3D3 and A5C5B5D5 are all squares.

8. Now to show similarity of squares [see Fig. 3], measure A1C1, A2C2, A3C3, A4C4, A5C5, C1B1, C2B2, C3B3, C4B4, C5B5 and so on.

Also, find ratios of their corresponding sides such as   

Observations & calculations

By actual measurement:

A2C2 = 2 ,  A4C4 = 4

C2B2 =2,   C4B4 = 4

B2D2 = 2,   B4D4 = 4

D2A2 = 2,   D4A4 = 4.

 

 

 

 

Also A₂ = 90^o , B₂ = 90^o , C₂ = 90^o , D₂ = 90^o , 

          A₄ = 90^o , B₄ = 90^o , C₄ = 90^o , D₄ = 90^o ,

Therefore, square A2C2B2D2 and square A4C4B4D4 are SIMILAR.

Similarly, each square is SIMILAR to the other squares.

Result

From this activity we conclude that all squares are similar to each other.

Applications.

Concept of similarity can be used in enlargement or reduction of images like maps in atlas and also in making photographs of different sizes from the same negative.

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