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  • IIt is given that triangleABC cong triangleFDE and AB = 5 cm, angleB = 40° and angleA = 80°. Then which of the following is true?(A) DF = 5 cm,angleF = 60°(B) DF = 5 cm, angleE = 60°(C) DE = 5 cm, angleE = 60°(D) DE = 5 cm, \angleD = 40°

It is given that △ABC≅△FDE and AB=5 cm,∠ B=40∘ and ∠A=80∘. Then which of the following is true?
(A) DF=5 cm,∠F=60∘
(B) DF=5 cm,∠E=60∘
(C) DE=5 cm,∠E=60∘
(D) DE=5 cm,∠D=40∘

Answers (1)

Solution

In △ABC,∠A=80∘,∠B=40∘ and ∠C=x (assume)

∵∠A+∠B+∠x=180∘ (angle sum property of a triangle)

⇒80∘+40∘+x=180∘⇒x=180∘−120∘⇒x=60∘⇒DC=60∘∵△ABC≅△FDE

By ASA congruence relation

AB=FD,∠ A=∠F,∠ B=∠D

⇒DF=5 cm,∠F=80∘,∠B=40∘=∠D∵ Also, ∠C=∠E⇒∠E=60∘

Therefore, DF=5 cm,∠E=60∘

Hence option (B) is correct.

 

Posted by

infoexpert24

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