Question
In Figure. $DE = IH, EG = FI$ and $\angle\text{ E} = \angle\text{I}.$ Is $\triangle\text{DEF}\triangle\text{HIG}? $ If yes, by which congruence criterion?
✓
Answer
Given, $EG = FI$
$EG + GF = FI + GF [$adding $GF$ on both sides$]\ EF = IG$
In $\triangle\text{DEF}$ and $\triangle\text{HIG},$
$DE = IH [$given$]$
$EF = IG [$proved above$]$
$\angle\text{E}=\angle\text{I} [$given$]$
By $SAS$ congruence criterion, $\triangle\text{DEF}\cong\triangle\text{HIG}$
$EG + GF = FI + GF [$adding $GF$ on both sides$]\ EF = IG$
In $\triangle\text{DEF}$ and $\triangle\text{HIG},$
$DE = IH [$given$]$
$EF = IG [$proved above$]$
$\angle\text{E}=\angle\text{I} [$given$]$
By $SAS$ congruence criterion, $\triangle\text{DEF}\cong\triangle\text{HIG}$
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