Triangle Similarity

Triangle Similarity:

AA, SSS, and SAS

By Heather Eve

Similar

"Similar" in math means that two objects have the exact same proportion but may not be the same size. This symbol ~ means similar.

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PS--Don't forget to take notes as you go through this lesson!​

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Subject | Subject

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Multiple Choice

Two objects that are the same shape but not the same size are _______.

• Congruent
• Vertical
• Similar
• Complementary 

Similarity Postulates

--> You learned about CONGRUENCE Postulates in a previous unit. These are: SAS, ASA, AAS, SSS, and HL

--> Congruence postulates prove that two triangles are IDENTICAL in every way.

--> There are also SIMILARITY postulates which use some of the same criteria, but instead of proving the triangles are identical, they prove that they are SIMILAR​

Subject | Subject

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Similarity Postulate 1: AA

--> AA means "Angle Angle"

--> Two triangles with the SAME EXACT angle next to one other SAME EXACT angle will be similar to each other.

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(but not necessarily identical)​

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Subject | Subject

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Multiple Choice

If two figures are similar,

then the angles are _________________.

• proportional

• congruent

• complementary

• supplementary

Multiple Choice

State if the two triangles are similar by AA.

• Similar by AA

• Not Similar

Multiple Choice

State if the two triangles are similar by AA.

• Not Similar

• Similar but not by AA

• Similar by AA

Multiple Choice

State if the two triangles are similar by AA.

• Not Similar

• Similar but not by AA.

• Similar by AA

Multiple Choice

State if the two triangles are similar by AA.

• Not Similar

• Similar but not by AA

• Similar by AA

Similarity Postulate 2: SSS

--> SSS means "Side Side Side"

-->This one is different from congruence SSS!!! A triangle with a set of THREE sides that each have the SAME proportion to another triangle's matching sides.

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Subject | Subject

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Similarity Postulate 2: SSS

EXAMPLE!

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​ Each set of matching sides has the same proportion!

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2/1 from left to right

1/2 from right to left​​

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Subject | Subject

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Multiple Choice

Sides in similar figures must be __________.  

• Proportional

• Congruent

• Opposite Reciprocals

• Parallel

Multiple Choice

State if the triangles are similar by SSS.

• Similar but not SSS

• Not Similar

• Yes, by SSS

Multiple Choice

State if the triangles are similar by SSS.

• Yes, SSS Similarity

• Similar but not SSS

• Not Similar

Multiple Choice

State if the triangles are similar by SSS.

• Yes, SSS Similarity

• Similiar but not SSS

• Not Similar

Multiple Choice

State if the triangles are similar by SSS.

• Yes, SSS Similarity

• Similiar but not SSS

• Not similar

Multiple Choice

State if the triangles are similar by SSS.

• Yes, SSS Similarity

• Similar but not SSS

• Not Similar

Multiple Choice

State if the triangles are similar by SSS.

• Yes, SSS Similarity

• Similar but not SSS

• Not Similar

Similarity Postulate 3: SAS

--> SSS means "Side Angle Side"

-->This one is different from congruence SAS!!! It is also the trickiest one. It goes like this:

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*Two triangles with a matching pair of sides that have a certain proportion.

*Next to that side each triangle has an angle that is EXACTLY the same!

*Next to that angle both triangles have a side that is the same proportion as their first proportion!​​

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Subject | Subject

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Similarity Postulate 3: SAS

EXAMPLE!

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​ AB/DF--> 12/8 = 3/2 (first set of sides)

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50=50 (identical angle)

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CB/FE--> 24/16 = 3/2 (second set of sides)​

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Subject | Subject

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Multiple Choice

State if the triangles are similar by SAS.

• Similar but not SAS

• Yes, SAS Similarity

• Not similar.

Multiple Choice

State if the triangles are similar by SAS.

• Yes, SAS Similarity

• Similar but not SAS

• Not Similar

Multiple Choice

State if the triangles are similar by SAS.

• Yes, by SAS Similarity
• Similar but not SAS

• No, not similar

Multiple Choice

State if the triangles are similar by SAS.

• Yes, SAS Similarity

• Similar but not SAS

• Not Similar

Multiple Choice

State if the triangles are similar by SAS.

• Similar but not SAS

• Yes, SAS Similarity

• Not Similar

Multiple Choice

State if the triangles are similar by SAS.

• Yes, SAS Similarity

• Similar but not SAS

• Not Similar

Putting It All Together!

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Can you tell WHICH postulate is the right one, or if any of them even apply at all?

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Be careful! Some of these questions require you to analyze the picture carefully and think about what the triangles have in common!​

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Subject | Subject

Some text here about the topic of discussion

Multiple Choice

State if the triangles in each pair are similar. If so, state how you know they are similar.

• Yes, AA Similarity

• Yes, SSS Similarity

• Yes, SAS Similarity

• Not Similar

Multiple Choice

State if the two triangles are similar and the rule that applies.

• Not Similar

• Similar by SAS

• Similar by AA

• Similar by SSS

Multiple Choice

State if the two triangles are similar and the rule that applies.

• Not Similar

• Similar by SAS

• Similar by AA

• Similar by SSS

Multiple Choice

State if the two triangles are similar and the rule that applies.

• Not Similar

• Similar by SAS

• Similar by AA

• Similar by SSS

Multiple Choice

State if the two triangles are similar and the rule that applies.

• Not Similar

• Similar by SAS

• Similar by AA

• Similar by SSS

Multiple Choice

State if the two triangles are similar and the rule that applies.

• Not Similar

• Similar by SAS

• Similar by AA

• Similar by SSS

Poll

After learning this topic, I feel....

• Excited or Happy 😀

• Overwhelmed or Confused 😵

• Sad or Disappointed 😭

• Angry or Frustrated 😡

• Meh (Not Great, Not Bad) 😐