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Congruence of Triangles and Inequalities in a Triangle — MATHS STD 9 — Question

Rajasthan BoardEnglish MediumSTD 9MATHSCongruence of Triangles and Inequalities in a Triangle1 Mark
Question
In $\triangle\text{ABC}$ and $\triangle\text{DEF,}$ it is given that $\angle\text{B}=\angle\text{E}$ and $\angle\text{C}=\angle\text{F}.$ In order that $\triangle\text{ABC}\cong\triangle\text{DEF},$ we must have:
  1. AB = DF
  2. AC = DE
  3. BC = EF
  4. $\angle\text{A}=\angle\text{D}$
✓

Answer

  1. BC = EF
Solution:
 
In $\triangle\text{ABC}$ and $\triangle\text{DEF},$
$\angle\text{B}=\angle\text{E}$ and $\angle\text{C}=\angle\text{F}$
So, the induded sides should be equal for the triangle to be congruent by the ASA congruence criterion.
Thus, we must have BC = EF.

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