Question

In ∆ ABC and ∆ DEF,it is given that AB=DE and BC=EF in order that ∆ ABC=~ ∆ DEF,me must have​

Answer 1

Step-by-step explanation:

AC=DF or angle A=angle D

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Answer 2

Given :- In ∆ABC and ∆DEF,it is given that AB=DE and BC = EF .

To Find :- In order that ∆ABC ≅ ∆DEF, we must have ?

Solution :-

Case 1) :- Assume AC = DF .

So, In ∆ABC and ∆DEF we have,

→ AB = DE { given }

→ BC = EF { given }

→ AC = DF { Assume }

since all three sides of ∆ABC are equal to three sides of ∆DEF, then the triangles are congruent .

then,

→ ∆ABC ≅ ∆DEF { By SSS congruence rule . }

Case 2) :- Assume ∠ABC = ∠DEF

So, In ∆ABC and ∆DEF we have,

→ AB = DE { given }

→ ∠ABC = ∠DEF { Assume }

→ BC = EF { given }

since two sides and the angle formed by these two sides of ∆ABC are equal to two sides and the included angle of ∆DEF, then the triangles are congruent .

then,

→ ∆ABC ≅ ∆DEF { By SAS congruence rule . }

therefore, we can conclude that, in order for ∆ABC ≅ ∆DEF we must have :-

• AC = DF .
• Or,
• ∠ABC = ∠DEF .

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