1. line AM is parallel to line NG and line AO is congruent to line NO : Given
2. angle A is congruent to angle N : alternate interior angles
3. angle AOM is congruent to angle NOG : Vertically opposite angles
4. Triangle AMO is congruent to triangle NGO : ASA postulate of congruency.
Congruent triangles have equal sides and angles, ensuring they are identical when superimposed. Corresponding angles and sides are congruent, denoted by matching markings.
This geometric property allows for precise comparisons and deductions in triangle relationships.
To prove that triangle AMO is congruent to triangle NGO ;
1. line AM is parallel to line NG and line AO is congruent to line NO : Given
2. angle A is congruent to angle N : alternate interior angles
3. angle AOM is congruent to angle NOG : Vertically opposite angles
4. Triangle AMO is congruent to triangle NGO : ASA postulate of congruency.