EDSC 121 - Inequality in Two Triangles
Hinge Theorem (SAS Inequality Theorem)
Hinge Theorem (SAS Inequality Theorem)
If two sides of one triangle are congruent to two sides of a second triangle, and the included angle in the first triangle is greater than the included angle in the second, then the third side of the first triangle is longer than the third side of the second.
In our case, Lines AC and AD are congruent, and the same is true for lines AB and BA. The only difference is their angles. If we increase angle CAB, line CB will also increase, and the same goes for angle DAB and line DB.
Converse of Hinge Theorem (SAS Inequality Theorem)
Converse Hinge Theorem (SAS Inequality Theorem)
If two sides of one triangle are congruent to two sides of a second triangle, and the third side of the first triangle is longer than the third side of the second, then the included angle in the first triangle is larger than the included angle in the second triangle..
It is the reverse of the normal Hinge Theorem, in a sense; instead of an angle to side, this one is a side to an angle.
In our case, if we manipulated point F or point C, whether to decrease or to increase it, the angles B and E also changes proportionally.