The Calabi triangle, which is the only non-equilateral triangle for which the largest square that fits in the interior can be positioned in any of three different ways, is obtuse and isosceles with base angles 39.1320261 . . . ?and third angle 101.7359477 . . . ?
22.
The theorem is named after Thales because he was said by ancient sources to have been the first to prove the theorem, using his own results that the base angles of an isosceles triangle are equal, and that the sum of angles in a triangle is equal to 180?
23.
The term \ scriptstyle \ frac { \ pi-\ theta } { 2 } represents the base angle of the triangle and is this value because the sum of the internal angles of any triangle ( in this case the two base angles plus " ? " ) are equal to " ? ".
24.
The term \ scriptstyle \ frac { \ pi-\ theta } { 2 } represents the base angle of the triangle and is this value because the sum of the internal angles of any triangle ( in this case the two base angles plus " ? " ) are equal to " ? ".
25.
Then we " slide " the left side of the line to the right to form a triangle . ( We can do this because the top and bottom lines are parallel ) Now the triangle has equal base angles, so the sides are isosceles .-- Lemontea 02 : 48, 20 May 2006 ( UTC)
26.
Some modern treatments ( not Euclid's ) of the proof of the theorem that the base angles of an isosceles triangle are congruent start like this : Let ABC be a triangle with side AB congruent to side AC . " Draw the angle bisector of angle A and let D be the point at which it meets side BC ".
