question_answer

In figure, DE = IH, EG = FI and \[\angle \]E = \[\angle \]I. Is\[\Delta DEF\cong \Delta HIG\]?

If yes, by which congruence criterion?

Answer:

Given, EG = FI adding GF on both sides, we get \[\therefore \] EG + GF = GF + FI EF = GI   ...(i) [from figure] In\[\Delta DEF\text{ }and\text{ }\Delta HIG\], DE - IH           [given] \[\angle DEF-\angle HIG\]               [given] and           EF = GJ           [from (i)] Here, we see that, if two sides and the angle included between them of a triangle are equal to two corresponding sides and the angle included them of other triangle, then the triangles are congruent by SAS congruence rule. Hence,