Angles opposite to equal sides of a triangle are equal.

If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles.

The bisectors of two equal angles of a triangle are equal.

If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles triangle.

The two altitudes corresponding to two equal sides of a triangle need not be equal.

If any two sides of a right triangle are respectively equal to two sides of other right triangle, then the two triangles are congruent.

Two right triangles are congruent if the hypotenuse and a side of one triangle are respectively equal to the hypotenuse and a side of the other triangle.