1. a scalene triangle cannot have 2 congruent angles.
For contradiction, assume that a scalene triangle
(a triangle has no sides congruent and has two congruent angles.
If two angles of a triangle are congruent, the sides opposite these angles are congruent.
That contradicts the assumption that it has no sides congruent.
2. an isosceles triangle cannot have a base angle that is a right angle.
For contradiction, assume that isosceles triangle ABC has congruent legs
AB and AC, and base angle A that is a right angle.
The base angles A and B of an isosceles triangle are congruent.
Therefore base angles A and B are both right angles.
The base BC is perpendicular to the legs AB and AC
Two lines perpendicular to the same line are parallel.
AB and AC do not intersect because parallel lines do not intersect.
That contradicts the fact that we have a triangle ABC at all.
Edwin
