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Congruent Triangles — Maths STD 9 — Question

Maharashtra BoardEnglish MediumSTD 9MathsCongruent Triangles1 Mark
MCQ
In Fig. $\text{AB}\perp\text{BE}$ and $\text{FE}\perp\text{BE},$ If $\text{BC}=\text{DE}$ and $\text{AB}=\text{EF},$ then $\triangle\text{ABD}$ is congruent to: 
  • A
    $\triangle\text{EFC}$
  • B
    $\triangle\text{ECF}$
  • C
    $\triangle\text{CEF}$
  • ✓
    $\triangle\text{FEC}$
✓

Answer

Correct option: D.
$\triangle\text{FEC}$

$AB = EF$
$BC = DE$
$BC + CD = DE + CD \ ($adding $CD$ both sides$)$
$BC + CD = BD, DE + CD = CE$
So $BD = CE$
Now Consider $\triangle\text{ABD},\triangle\text{FEC}$
$\text{AB}=\text{FE}$
$\text{BD}=\text{EC}$
$\angle\text{ABD}=\angle\text{FEC}=90^\circ$
So $\triangle\text{ABD}\cong\triangle\text{FEC}$ by $\text{SAS}$ creterion.
Hence, correct option is $(d)$.

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