Question

It is given the ABC congruent FDE and AB=4 cm, angleB = 40' and angle E = 60',
then which of the following is true.
(A) DE=4 cm, ZA=80°
(B) DE = 4 cm, ZC=80°
(C) DF=4 cm, ZA=80°
(D) DF = 4 cm, ZC=80°


Please give me the answer

Answer 1

Given : ΔABC ≅ Δ FDE

AB = 4cm

∠B = 40°

∠E = 60°

To Find :  which is the following is true

(a) DE =4cm ,angle A = 80°

(b) DE=4cm , angle C= 80°

(c) DF=4cm, angle A=80°

(d)DF=4cm,angle C = 80 °​

Solution:

ΔABC ≅ Δ FDE

corresponding sides and angles are equal

AB = DF  =>  DF = 4 cm  

BC = DE

AC = FE

∠A = ∠F  =

∠B = ∠D =  40°

∠C = ∠E  =  60°

=> ∠A = ∠F  =  ( 180° - 40°  - 60°) = 80°

Hence correct option is :

(c) DF=4cm, angle A=80°

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