Mathematics Lab Activity-07 Class IX | Triangles

   Lab Activity-07 Class iX

Mathematics Lab Activities on Triangles for class IX students, with complete observation tables, strictly according to the CBSE syllabus.

Chapter - 07  Triangles

Activity - 07

Objective: 

To verify experimentally the different criteria for congruency of triangles using triangle cut-outs.

Material Required

Cardboard, scissors, cutter, white paper, geometry box, pencil/sketch pens, coloured glazed papers.

Procedure

1. Take a cardboard of a convenient size and paste a white paper on it.

2. Make a pair of triangles ABC and DEF in which AB = DE, BC = EF, AC = DF on a glazed paper and cut them out [see Fig. 1].

Figure 1

3. Make a pair of triangles GHI, JKL in which GH = JK, GI = JL, ∠G = ∠J on a glazed paper and cut them out [see Fig. 2].

Figure 2

4. Make a pair of triangles PQR, STU in which QR = TU, ∠Q = ∠T, ∠R = ∠U on a glazed paper and cut them out [see Fig. 3].

Figure 3

5. Make two right triangles XYZ, LMN in which hypotenuse YZ = hypotenuse MN and XZ = LN on a glazed paper and cut them out [see Fig. 4].

Figure 4

6. Superpose DABC on DDEF and see whether one triangle covers the other triangle or not by suitable arrangement. See that △ABC covers △DEF.

7. Completely only under the correspondence AD, B ↔ E, C ↔ F. So, △ABC ≌ △DEF, if AB = DE, BC = EF and AC = DF. This is SSS criterion for congruency.

8. Similarly, establish △GHI ≌ △JKL if GH = JK. ∠G = ∠J and GI = JL. This is SAS criterion for congruency.

9. Establish △PQR ≌ △STU, if QR = TU, ∠Q = ∠T and ∠R = ∠U. This is ASA criterion for congruency.

10. In the same way, △STU ≌ △LMN, if hypotenuse YZ = hypotenuse MN and XZ = LN. This is RHS criterion for right triangles.

Observations

On actual measurement :

In △ABC and △DEF,
AB = DE ....... Each = 3.5 cm

BC = EF ....... Each = 5 cm
AC = DF ....... Each = 4.5 cm

Therefore, △ABC ≌ △DEF by SSS ≌ rule

2. In △GHI and △JKL,
GH = JK, ....... Each = 3 cm 

GI = JL,   ....... Each = 6 cm 

∠G =  ∠J, .......Each = 40^o.

Therefore, △GHI ≌ △JKL by SAS ≌ rule

3 In △PQR and △STU,
QR = TU ....... Each = 6 cm

∠Q = ∠T = .......Each = 30^o.

∠R = ∠U = .......Each = 80^o. 
Therefore, △PQR ≌ △STU by ASA ≌ rule

4. In △XYZ and △LMN, 

Hypotenuse YZ = Hypotenuse MN ....... Each = 10 cm
XZ = LN = ....... Each = 8 cm
∠X = ∠L ....... Each = 90°

Therefore, △XYZ ≌ △LMN by RHS ≌ rule

Result : 

Here we see that triangles are congruent by SSS, SAS, ASA and RHS congruence rule.

Applications

These criteria are useful in solving a number of problems in geometry. These criteria are also useful in solving some practical problems such as finding width of a river without crossing it.

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