We call two figures congruent if their corresponding sides and angles are equal. Let \(ABD\) an \(A'B'D'\) be two right-angled triangles with right angle \(D\). Then if \(AD=A'D'\) and \(AB=A'B'\) then the triangles \(ABD\) and \(A'B'D'\) are congruent.
It follows from the previous statement that if two lines \(AB\) and \(CD\) are parallel than angles \(BCD\) and \(CBA\) are equal.
We prove the other two assertions from the description:
The sum of all internal angles of a triangle is also \(180^{\circ}\).
In an isosceles triangle (which has two sides of equal lengths), two angles touching the third side are equal.