5.6 Hinge Theorem and its Converse

Hinge Theorem (Inequalities in 2 Triangles)

What's the relation between side [i]AB [/i]to side [i]DE[/i], and [i]BC [/i]to [i]EF[/i]?

Move vertices [i]C[/i] and [i]F[/i]. What conclusion can you make when angle[i] B[/i] is greater than angle [i]E[/i]?[br]Hint: observe the side opposite to angles [i]B[/i] and [i]E[/i].

This is an example of Hinge theorem. Play around with the triangle. Another name for the [i]Hinge Theorem[/i] is [i]SAS inequality.[/i] Why do you think it is also called [i]SAS Inequality[/i]?

What conclusions can you make about angles [i]B[/i] and [i]E[/i] when side [i]DF [/i]is greater than side [i]AC[/i]?

Another name for the [i]Converse of the Hinge Theorem[/i] is [i]SSS inequality.[/i] Why do you think it is also called [i]SSS Inequality[/i]?

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Information: 5.6 Hinge Theorem and its Converse