Problems

• We call two figures congruent if their corresponding sides and angles are equal. Let $ABD$ an $A^{\prime }{B}^{\prime }{D}^{\prime }$ be two right-angled triangles with right angle $D$. Then if $AD=A^{\prime }{D}^{\prime }$ and $AB=A^{\prime }{B}^{\prime }$ then the triangles $ABD$ and $A^{\prime }{B}^{\prime }{D}^{\prime }$ 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.