Question

it is given the triangle ABC= triangle FDE and AB = 4cm,angle B=40° and angle E=60° the which of the following is true​

Answer 1

HELLO DEAR,

QUESTION:-it is given the triangle ABC= triangle FDE and AB = 4cm,angle B=40° and angle E=60° the which of 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°

GIVEN:- ∆ABC ≅ ∆ FDE

angleB = 40°

angleE = 60°

AB. = 4cm

ANSWER:-(C) DF = 4cm , angle A = 80°

∆ ABC ≅ ∆ FDE

The both triangle are congurence ,so according to the congurency corresponding parts and angles of congurence triangle are same.

AB = FD = 4cm

AB = 4cm , FD = DF = 4cm.

And angleA = angle F

angle B = angle D = 40°

angle C = angle E = 60°

So, in ∆ABC,

(angle A + angle B + angle C)= 180°

( angleA + 40° + 60°) = 180°

(angleA + 100°) = 180°

angleA = 180° - 100°

angleA= 80°.

Therefore ,(C) DF = 4cm , angle A = 80°.

I HOPE IT'S HELP YOU DEAR,

THANKS.

Answer 2

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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Step-by-step explanation: