6.4/6.5 Triangle Similarity by AA, SSS, and SAS

6.4/6.5 Triangle Similarity

​LO: SWBAT use similarity theorems to prove that two triangles are similar


DOL: Using triangle similarity theorems SWBAT state whether triangles are similar with a 70% accuracy rate.

Similar Polygon Key Points

​Similar Polygons have congruent angle and proportional sides.

Congruent Polygons have congruent angles and congruent sides

​Similarity Symbol: ∼

Similarity Statement: ΔABC ∼ΔDEF

The 3 Similarity Shortcuts

Example: AA Similarity

​When I am using AA Similarity I am looking for two sets of corresponding angles that are congruent.

Multiple Choice

Do the two triangles fit the AA Similarity Postulate

• Yes

• No

Multiple Choice

Do the two triangles fit the AA Similarity Postulate

• Yes

• No

Example: SSS Similarity

​With SSS Similarity I am looking to prove that all the side ratios are the same.

Multiple Choice

Determine if ΔABC ∼ ΔGHJ

Hint: Check if all the side ratios are the same.

• They are similar

• They are not similar

Multiple Choice

Determine if ΔABC ∼ ΔDEF

Hint: Check if all the side ratios are the same.

• They are similar

• They are not similar

Example: SAS Similarity

​With SAS Similarity we want to find that two sets of corresponding sides are proportional and that the included corresponding angles are congruent

Multiple Choice

Can we use the SAS Similarity Theorem to prove the two triangles are similar?

• Yes

• No

Multiple Choice

Explain how to show that the indicated triangles are similar

• SSS

• SAS

• AA

• Not Enough Information

Multiple Choice

Verify that ΔABC ∼ ΔDEF. Find the scale factor of ΔABC to ΔDEF.

• Similar

  SF = 2 : 3

• Similar

  SF = 3 : 2

• Not Similar