Question

ABDF is a square and BC = EF in the given figure. Prove that

(i) ∆ABC≊ ∆​AEF

Answer 1

Answer:

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Step-by-step explanation:

In ∆AEF and ∆ACF,

ANGLE AFE = ANGLE AFC

EF = CF

THEREFORE, ∆AEF =~ ∆ ACF BY RHS CONGRUENCE

HENCE AE = AC BY CPCT

SO,IN ∆ ABC AND ∆AEF

FE = BC GIVEN

AE = AC PROVED

AF = AB BY SQUARE RULE.

THEREFORE, ∆ABC =~ ∆ AEF

PROVED

Answer 2

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Given,

BC=EF

Since ABCD is a square, sides are equal

AF=AB

∠B=∠F

Therefore from SAS theorem

ABC≅AFE

⟹AC=AE Hence the triangle is isoceles.

AEG≅ACG

Therefore from ASA theorem

ACG≅AEG
Hope it helps you