was used is to notice if the number got bigger or smaller. Is that what we expected to happen?
Update the List of Symbols –In previous lessons it has been recommended that students create a reference page
in their note books that contains a list of all the symbols and how they are being used in this class. Students
should add the symbol for similar to the list, and take few minutes to compare it to the symbols they already know.
Sometimes students will read the similarity symbol as “approximately equal”. It is standard to use two wavy lines
for approximately equal and one wavy line for similar, but this is not always the case.Similarity by AA
Definition of Similar Triangles vs. AA Shortcut –Let the students know what a deal they are getting with the
AA Triangle Similarity Postulate. The definition of similar polygons requires that all three corresponding pairs of
angles be congruent, and that all three pairs of corresponding sides are proportional. This is a significant amount of
information to verify, especially when writing a proof. The AA postulate is a significant shortcut; only two piece of
information need to be verified and all the rest comes for free. When students see how much this reduces the work,
they will be motivated to understand the proof and will enjoy using the postulate. Everybody likes to use a tricky
shortcut.
Get Some Sun –It is always a good idea to create some variety in the class. It will keep students’ minds active.
Although it is time consuming, get some yard sticks and take the students outside to measure a tree or a flagpole
using their shadows and similar triangles. Have them evaluate their accuracy. They will have to measure carefully
if they are to get a reasonable numbers. This will give them some practice using a rule and converting units. The
experience will also help them put what they are learning about similar triangles into their long term memory.
Trigonometry –Let the students know that the next chapter is a about trigonometry, and that the AA Triangle
Similarity Postulate is what make trigonometry possible. If the students know what an important postulate this is,
they will be motivated to understand and learn how to apply it. Mentioning what is to come will start to prepare their
minds and make learning the material in the next chapter that much easier. Here are some problems that involve
similar right triangles to accustom the students to this new branch of mathematics.
Key Exercises:- 4 ABCis a right triangle with right angleC, and 4 ABC∼4XY Z.
Which angle in 4 XY Zis the right angle?
Answer:^6 Z - 4 CAT∼4DOG,^6 Ais a right angle
CA=5 cm,CT=13 cm
What isDG?
Answer:DG=13 cm,
Students must use the Pythagorean theorem and the definition of similar polygons.Similarity by SSS and SAS
The[U+0080][U+009C]S[U+0080][U+009D]of a Triangle Similarity Postulate –At this point in the
class, students have shown that a significant number of triangles are congruent. They have learned the process well.
When teaching them to show that triangles are similar, it is helpful to build on what they have learned. The similarity
postulates haveS′s andA′s just like the congruence postulates and theorems. TheA′s are treated exactly the sameChapter 2. Geometry TE - Common Errors