Concept of Similarity in Geometry

Remember when you learned what congruence is? Well, similarity is similar (no pun intended :-) )! The intuition for congruence is same shape, same size. Now guess what the intuition for similarity is? Same shape, different size! That's it! So, for example, all circles are similar to each other. Can you think of any other examples? Yes, all regular polygons. It seems like you understand now, good job! Here is a worksheet to practice your newly acquired skills, just on triangles: http://cdn.kutasoftware.com/Worksheets/Geo/7-Similar Triangles.pdf

Good luck and have fun!

Similarity

Two objects are similar if they are similar in all aspects except possibly size or orientation. If the two objects are congruent up to a dilation, then they are also similar.

All circles are similar to each other.

Two triangles are similar if they have two equal angles (also known as AA similarity), or if their corresponding sides have an equal ratio.

In general, two polygons are similar if their corresponding angles are equal and corresponding sides are in a fixed ratio. Both of the conditions must be satisfied for polygons with four or more sides to be similar.

This is very intuitive. Similarity transformations are when the image of the transformation is similar to the original object. By the definition of similarity, the distances have a scale factor/ratio of the distances (sides, diagonals, etc.)

Remember, what is a segment? A segment is a line with 2 endpoints. Figures are similar if all its angles are equal and its lengths are in proportion. Segments do not have angles, so we don't have to worry about those! But what about their lengths? How many lengths do segments have? Just one! So, in conclusion, all segments are similar since their lengths are in proportion.