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Construct a ΔPET, PE = 4.5 cm, ET = 5.4 cm and TP = 6.5 cm in your notebook. Now construct ΔABC, AB = 5.4 cm, BC = 4.5 cm and CA = 6.5 cm on a piece of paper. Cut it out and place it on the figure you have constructed in your notebook. Are the triangles congruent ? Write your answer using mathematical notation.

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ΔPET, PE = 4.5 cm, ET = 5.4 cm, TP = 6.5 cm. 

Step – 1 : 

Draw a rough sketch of the triangle and label it with the given measurements. 

Step – 2 : 

Draw a line segment PE of length 4.5 cm. 

Step – 3 : 

With centre P, draw an arc of radius 6.5 cm. 

Step – 4 : 

Draw another arc from E with radius – 5. 4 cm such that it intersects first arc at T. 

Step – 5 : 

Join P, T and E, T. 

The required APET is constructed.

ΔABC, AB = 5.4 cm, BC = 4.5 cm and CA = 6.5 

Step – 1 : 

Draw a rough sketch of the triangle and label it with the given measurements. 

Step – 2 : 

Draw a line segment AB of length 5.4 cm. 

Step – 3 : 

With centre A, draw an arc of radius 6.5 cm. 

Step – 4 : 

Draw another arc from B with radius 4.5 cm such that it intersects first arc at C. 

Step – 5 : 

Join A, C and B,C. 

The required AABC is constructed. If we place the ΔABC on ΔPET, the triangles are congruent. This is because, AB = TE AC = PT BC = PE 

∴ ΔABC ≅ ΔTEP (SSS criteria)

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