Question

If ABC and DEF are two triangles such that Δ ABC≅ Δ FDE and AB =5 cm, ∠B = 40° and ∠A =80°, Then, which of the following is true?
A. DF = 5 cm, ∠F= 60°
B. DE = 5 cm, ∠E= 60°
C. DF = 5 cm, ∠E= 60°
D. DE = 5 cm, ∠D= 40°

Answer 1

Concept :  

Congruence of triangles :  

• Two triangles are congruent, if sides and angles of a triangle are equal to the corresponding sides and angles of the triangle.  
• In Congruent triangles, corresponding parts are always equal and we write it in short 'CPCT', i e, Corresponding Parts of Congruent Triangles.
• It is necessary to write a correspondence of vertices correctly for writing the congruence of triangles in symbolic form.

 

Given :  ABC and DEF are two triangles such that Δ ABC≅ Δ FDE and AB = 5 cm, ∠B = 40° and ∠A = 80°.

In ∆ ABC ,

By angle sum property :  

∠A + ∠B + ∠C = 180°

80° + 40° + ∠C = 180°

120° + ∠C = 180°

∠C = 180° - 120°

∠C = 60° ………(1)

Δ ABC≅ Δ FDE  

6 pairs of corresponding parts of the two triangles congruent :  

AB = DF = 5 cm  

BC  = DE

AC = FE

∠A = ∠F = 80°  

∠B = ∠D = 40°

∠C = ∠E = 60° (from eq 1)

Hence, side DF = 5 cm , ∠E = 60°  

Option (C) DF = 5 cm , ∠E = 60° is correct.

HOPE THIS ANSWER WILL HELP YOU…..

 

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