Hinge Theorem and its Converse

Triangle [color=#0000ff]ABC[/color] and [color=#ff7700]DEF[/color] have two pairs of [color=#ff00ff]congruent[/color] [color=#9900ff]corresponding [/color]sides.[br][b]Select all the correct statements.[/b]

[color=#9900ff]AB[/color] = [color=#9900ff]DE[/color] [color=#ff00ff]AC[/color] = [color=#ff00ff]DF[/color] [color=#ff00ff]AC[/color] = [color=#9900ff]DE[/color] [color=#9900ff]AB[/color] = [color=#ff00ff]DF[/color]

Move [color=#0000ff]point C[/color] so that [color=#0000ff]angle A becomes larger and smaller[/color].[br][b]What do you notice about how this affects the [color=#0000ff]length of the opposite side BC[/color]?[/b]

Adjust [color=#0000ff]point C[/color] so that [color=#0000ff]angle A has a measure of approximately 30 degrees[/color].[br]Adjust [color=#ff7700]point F[/color] so that [color=#ff7700]angle D has a measure of approximately 45 degrees[/color].[br][b]Which statement is correct?[/b]

[color=#0000ff]BC[/color] [math]>[/math] [color=#ff7700]EF[/color] [color=#0000ff]BC[/color] [math]<[/math] [color=#ff7700]EF[/color]

Adjust [color=#0000ff]point C[/color] so that [color=#0000ff]side BC has a length of approximately 6 units[/color].[br]Adjust [color=#ff7700]point F[/color] so that [color=#ff7700]side EF has a length of approximately 4 units[/color].[br][b]Which statement is correct?[/b]

[i][color=#0000ff]m[/color][/i][math]\angle[/math][color=#0000ff]A[/color] [math]>[/math] [i][color=#ff7700]m[/color][/i][math]\angle[/math][color=#ff7700]D[/color] [i][color=#0000ff]m[/color][/i][math]\angle[/math][color=#0000ff]A[/color] [math]<[/math] [i][color=#ff7700]m[/color][/i][math]\angle[/math][color=#ff7700]D[/color]

Which statement(s) is a correct conclusion of this exploration?

If two triangles have two pairs of corresponding congruent sides, then the triangle with the larger third side will have the larger included angle. If two triangles have two pairs of corresponding congruent sides, then the triangle with the larger included angle will have the larger opposite side.

Hinge Theorem and its Converse

Information: Hinge Theorem and its Converse