Given two triangles ABC and DEF which satisfy the following:

1) |AC| = |DF|
2) |AB| = |DE|
3) /ABC = /DEF > 90°

Prove or disprove that the triangles are congruent.

With the usual notation...

The cosine rule gives b² = a² + c² - 2ac cosB which can be written as

a² - (2c cosB)a + c² - b² = 0. The sum of the roots of this quadratic in ‘a’

will therefore be 2c cosB. Since this is less than zero when B is obtuse, it

follows that, at most, only one of the roots can be positive. i.e. a triangle defined

by the values b, c and B (obtuse) can have only one possible value for ‘a’ so that

the triangles ABC and DEF are congruent SSS.

Posted by Harry on 2010-11-02 13:44:38