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Book 8 Answers to Mathematics Review Questions
As shown in the figure, in triangles ABC and △DEF, AB=DE, AC=DF, AM=EN, and M and N are the midpoint of sides AC and DF, respectively.

Verify △ ABC△ def

It is proved that ∵MN is the midpoint of AC edge and DF edge, AC=DF, ∴AM=CM=DN=FN,

At △ABM and △DEN,

AB=DE

{BM=EN

AM=DN

∴△ABM≌△DEN(SSS)

∴∠AMB=∠DNE (the corresponding angles of congruent triangles are equal).

∴∠BMC=∠ENF (complementary angles of equal angles are equal)

BM = EN,CM=FN。

∴△BMC≌△ENF(SAS)

∴BC=EF (the corresponding sides of congruent triangles are equal)

AB = DE,AC=DF。

∴△ABC≌△DEF(sss)