Given a line L in a plane and a point P which is in the plane but is not on the line L, there is exactly one line in the plane passing through P which is parallel to L.
for each point P of the plane, F assigns a point F(P) to P satisfying the distance preserving property, that is, for any two points A and B, the distance between A and B is equal to the distance between F(A) and F(B)
|AB| = |F(A)F(B)|.
Given two triangles △ABC and △A0B0C0 so that |AB| = |A0B0|, |∠A| = |∠A0|and|∠B| = |∠B0|, △ABC ∼ = △A0B0C0
Given two triangles ABC and A0B0C0 so that |∠A| = |∠A0|, |AB| = |A0B0|, and |AC| = |A0C0|, then △ABC ∼ = △A0B0C0.
Two triangles with three pairs of equal sides are congruent.
If two right triangles have equal hypotenuses and one pair of equal legs, then they are congruent.