Triangle similarity: Definition, criteria and demonstrations
Definition
Two triangles are similar if and only if they have the three angles congruently arranged. Also, the equivalent sides must be proportional.
Similar triangles
Analysis 1
Change the positions of points A, B, C, A', B' or C'. What do you see regarding the value of k?
Analysis 2
Change the positions of points A, B, C, A ', B' or C 'so that k is equal to 1. What can you notice about the triangles?
1st Similarity Case: ANGLE-ANGLE SIMILARITY
2nd Similarity Case: Side-Angle-Side
Exercise
Find a reason for the use of theorem in the previous demonstration: "If a line divides two sides of a triangle
and determines segments proportional to those two sides, then it is parallel to the third side." Use the following figure as reference.
