Question

Question 151

In the given figure, DE = IH, EG = FI and $\angle E=\angle I$. Is $\Delta DEF\cong \Delta HIG$? If yes, by which congruence criterion?

Answer 1

Given, EG = FI
EG + GF = FI + GF [adding GF on both sides]
EF = IG
In $\Delta DEF$ and $\Delta HIG$, DE = IH [given]
EF = IG [proved above]
$\angle E=\angle I$ [given]
By SAS congruence criterion, $\Delta DEF\cong \Delta HIG$