Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.




This is where we define what it means to be similar and then
using the definition of similarity transformations we will discuss corresponding angles and sides. We will look at the proportionality of corresponding parts, the congruence of corresponding angles and the writing of similarity statements. This process is parallel to what we did for congruence in G.CO.B.6 and G.CO. B.7 but now we are doing it again for similarity.






(1) The student will be able to identify corresponding angles and sides based on similarity statements.


(2) The student will be able to develop and write similarity statements for two polygons.


(3) The student will be able to determine if two triangles are similar based on their corresponding parts.


(4) The student will be able to establish a sequence of similarity transformations between two similar polygons.






If we can identify two polygons to be the product of dilation then the corresponding sides will be proportional and the angles will be congruent. Dilations create similarity in shapes. Here is an example of dilating segment BD. Notice the classic diagram with parallel lines because dilations form parallel lines.






In G.CO.A.2 we introduced the topic of isometric transformations and dilations were discussed lightly as one of the transformations that altered the size but not the shape of figure. This was early ground work on the concept of similarity.



We need to learn the definition of what makes two shapes similar so that we can establish relationships within the shapes. Knowing that two shapes are similar will open the door to determine lengths using ratios and knowing angles due to their corresponding congruence.



Usually the most difficult part of similarity is creating the correct ratio/scale factor for the given relationship. It isn't always easy to identify which segments correspond with each other. Unfortunately, if you set the relationship up wrong then so will be the final answer.






MY REFLECTIONS (over line l)

Generally, most of this objective is quite simple to the students. It is so 'similar' to what we did with congruence it makes sense. They already know that when writing a similarity statement that the names of each figure must relate the corresponding parts.