Investigating Triangle Similarity Theorems
In previous classes, to prove that two triangles are congruent you needed to prove that the triangles had 3 sets of corresponding congruent angles AND 3 sets of corresponding proportional sides. This activity will help you to discover the "shortcuts" to proving two triangles are similar.
Table of Contents
- SAS Similarity
- SAS Triangle Similarity Theorem
- AA Similarity
- AA Similarity AM
- SSS Similarity
- SSS Similarity Investigation (AM)
SAS Triangle Similarity Theorem
In the triangles below..[br]There is 1 set of corresponding congruent angles (Angle C & Angle F)[br]AND[br]There are 2 sets of corresponding proportional sides (AC/DF & BC/EF)
Name and perform the transformation the will map C onto F.
Name and perform the transformation that will map C'B' onto EF. (Hint: The measure of Angle B'C'E is 80 degrees.)
Name and perform the transformation that will map C"A" onto DF.
Lastly, name and perform the operation that maps B''' onto E. (Hint: The scale factor is 2.)
How do you know that this last transformation will also map A''' onto D?
AA Similarity AM
What do the two triangles have in common?
Name and perform the transformation that maps C onto F.
Name and perform the transformation the maps B'C' onto EF. (Hint: The measure of Angle B'C'E is 80 degrees)
Name and perform the transformation A"C" onto DF.
Lastly, name the transformation that maps B''' onto E. (Hint: Use scale factor of 2)
Why does this transformation also map A''' onto D?
SSS Similarity Investigation (AM)
What do you notice about the side lengths of the triangles above?
What do you notice about the angle measures in the triangles above?
Now, adjust the scale factor. What do you notice about the sides and angles?