Question
In $\triangle\text{ABC}$ and $\triangle\text{DEF,}$ it is given that AB = DE and BC = EF. In order that $\triangle\text{ABC}\cong\triangle\text{DEF},$ we must have:
  1. $\angle\text{A}=\angle\text{D}$
  2. $\angle\text{B}=\angle\text{E}$
  3. $\angle\text{C}=\angle\text{F}$
  4. none of these

Answer

  1. $\angle\text{B}=\angle\text{E}$

Solution:

In $\triangle\text{ABC}$ and $\triangle\text{DEF},$

AB = DE and BC = EF

SO, the induded angles should be equal for the triangle to be congurent by the SAS congruence criterion.

Thus, we must have $\angle\text{B}=\angle\text{E}.$

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