What Similar Triangles Are Congruent?

Over many centuries we have been using the similarity theorems. You would use this when you are farmers(forest, conservation, and logging), construction workers(glazers and roofers), insolation(electricians), production(mechanics), and a lot of professional works such as computer and mathematical occupations, architects, and engineers. When trying to prove that two triangles are congruent you first have to figure out if they have congruent sides and angles. TO figure out if they are similar you have to figure out if the sides and angles are congruent. The different theorems are commonly known as the Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Angle-Side-Angle (AAS), Angle-Angle (AA) and Hypotenuse-Leg (HL). The others

Side Angle Side states that two sides and one angle is congruent to two sides and one angle of another triangle. The Angle Angle Side theorem states that two angles and the non-included side of two angles is congruent to the corresponding parts of another triangle. The Hypotenuse leg theorem states that the hypotenuse and the leg of one right triangle is congruent to the corresponding parts on the opposite side of the triangle. The triangle proportionality theorem states that if one line is parallel to one side of a triangle and intersects the other two sides of the triangle then the line divides the triangle

The second one states that each leg is the geometric mean between the hypotenuse and the segment of the hypotenuse that is adjacent to the leg. The pythagorean theorem states that one of the angles is always equal to 90 degrees. The converse of the pythagorean theorem states that one of the squares of one side of a triangle will be equal to the sum of the other sides of the triangle which proves that the triangle is a right triangle. The triangle angle bisector theorem states that if a ray bisects a triangle then it divides the opposite side into segments that are proportional to the other side. The 30-60-90 states that the sides are a ratio of 2:1. The 45-45-90 states that the ratio of the sides are 1;1;√2. A right Acute is when a^2 +b^2 is greater that c^2. A right obtuse is when a^2=b^2 is less than c^2. A right right is when a^2+b^2 is equal to c^2. The last theorem is CPCTC. This stands for Corresponding parts of congruent triangles are congruent. You would use this when you are trying to figure out if two triangles are congruent. You would use this if you already knew that the triangles were congruent. This would help prove that corresponding sides and angles are congruent. This theorem is to be used after you prove two triangles congruence. This states that each part of one triangle is congruent to each corresponding part of the other triangles. When trying to figure out if two triangles are congruent