explain why you need to prove 2 angles congruent before you can prove the parts of the triangles congruent.
In geometry, if two triangles have two angles that are congruent, then it can be concluded that the third angles are also congruent due to the fact that the sum of the angles in a triangle is always 180 degrees. This property is known as the Angle-Angle (AA) postulate.
When proving triangles congruent, it is essential to establish the congruence of two angles first in order to ensure that the triangles are similar in shape. If two angles are congruent, it indicates that the sides of the triangles are also proportional and that the triangles are similar. This in turn allows for the corresponding sides of the triangles to be proven congruent, leading to the overall congruence of the two triangles.
Therefore, proving two angles congruent is crucial in establishing the similarity of the triangles, which is a prerequisite to proving the corresponding parts of the triangles congruent.