prove that If two angles and one side of one triangle are equal to two angles and the corresponding side of the other triangle ,then the two triangles are congruent.
Answers
Answer:
Given: Two triangles ABC and DEF such that B = E, C = F
and BC = EF. To prove: ABC DEF
Step-by-step explanation:
Proof: Case I: If AB = DE then in ABC and DEF, AB = DE [by supposition] BC = EF [given] and B = E [given] Thus, ABC DEF [SAS criterion] Case II: If AB < DE Take a point G on ED such that EG = AB. Join GF. In ABC and GEF, we have AB = GE [by supposition] BC = EF [given] B = E [given] Thus, ABC GEF [SAS criterion] ACB = GFE [corresponding parts of congruent triangles are equal] But ACB = DFE [given] GFE = DFE, This is only possible when FG coincides with FD or G coincides with D. AB must be equal to DE and hence, ABC DEF (by SAS) Case III: If AB > ED With a similar argument (as in case II), we may conclude that ABC DEF (by SAS) Thus, ABC DEF.
It is very hard I will try next time