Third Angle Theorem
if two angles of one triangle are congruent to two angles of another triangle, then the third angles of the triangles are also congruent
The Third Angle Theorem is a theorem in geometry that states that if two triangles have two angles and the included side of one triangle congruent to the corresponding two angles and included side of the other triangle, then the third angles of the triangles are also congruent.
In simple terms, the Third Angle Theorem states that if two triangles are congruent in every respect except for the third angle, then the third angle must also be congruent.
This theorem can be proved using the fact that the sum of the angles in a triangle is always equal to 180 degrees. If two of the angles and the included side of one triangle are congruent to the corresponding two angles and included side of another triangle, then the third angle in each triangle must be such that the sum of the three angles is 180 degrees. Since two of the angles are already congruent, the third angle in each triangle must also be congruent.
The Third Angle Theorem is particularly useful in geometry because it allows us to prove that two triangles are congruent using less information. Instead of having to show that all three sides and angles of two triangles are congruent, we can simply show that two angles and an included side are congruent, and then use the Third Angle Theorem to show that the third angle is also congruent.
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