SSS and SAS Similarity

SSS and SAS Similarity

by Julia Slivnik

​SIDES ARE PROPORTIONAL

• ​If you can show all sides are proportional, the triangles are similar

• ​Proportional meaning all the ratios (fractions are equation)

Multiple Choice

Are these ratios proportional?

$$\frac{2}{3},\ \frac{8}{12},\ \frac{16}{23}$$  

• yes

• no

​Two sides are proportional and INCLUDED angle is congruent

• ​The angle HAS to be the angle that is in between the two proportional sides.

• ​Similar to SAS like we did before only the sides have to be proportional meaning the ratios have to be equal.

Open Ended

Given that these triangles are similar, please explain to me which sides are corresponding to each other. For example, I could say <B is congruent to <Q. However, I want you to tell me the corresponding sides.

​These are in your notes

​Still in your notes.....

​We only know two sides and an angles, so we should check SAS. HOWEVER, we have to make sure the angle is IN BETWEEN the two sides.

​In this case, the angle is in between the two sides and the angles are equal

​Still in your notes....

​This is an example where you cannot say they are similar because in the first triangle, the angle in NOT IN BETWEEN the two sides.

​

​Therefore, these triangles cannot be assumed to be similar

​OR

Multiple Select

Select the correct options

• $$Scale\ factor\ is\ \frac{3}{4}$$  

• $$\Delta WRS\sim\Delta TRV$$  

• Similar by SAS

• Similar by SSS

• Not Similar

​If you look at the vertical angles, they are NOT in between the sides

​

​The angles that should be equal should be <SWR and <RTV

Multiple Select

Select the correct responses

• $$\Delta MNL\sim\Delta QRP$$  

• Not Similar

• Similar by SAS

• Similar by SSS

• $$Scale\ factor\ is\ \frac{2}{3}$$  

​Again, not similar because the angle is not in between the sides in the first triangle.

​OR

Multiple Choice

• Not Similar

• Similar by SSS

• Similar by SAS

• Similar by AA

​The reason it was not AA is because we do not know that NP and RS are parallel

Multiple Choice

Which one is the correct similarity statement. Keep in mine. These are similar triangles based on SAS and AA

• $$\Delta QRP\sim\Delta SRT$$  

• $$\Delta RPQ\sim\Delta SRT$$  

• $$\Delta TRS\sim\Delta QRP$$  

• $$\Delta QPR\sim\Delta STP$$  

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​Then cross multiply.....

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​DRAW A PICTURE! RIGHT NOW! DRAW OUT THESE TRIANGLES

No assignment today​

Please make sure you have written this in ​your notes.

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​STAR TESTING IS TUESDAY AND CHAPTER TEST IS WEDNESDAY