Intro to Triangular Similarity

Intro to Triangular Similarity

by Coach Miller

Open Ended

Which one doesn't belong? WHY?

​This is what your notes will look like. We will go through each similarity statement for notes & examples

Congruence ​​v Similarity

​Congruence

​Same size, same shape

​

​Similarity

​same shape

​different size

​proportional (by ratio) side lengths

​ -corresponding sides have the same scale factor

​all angles are congruent (same)

beneficial to write down

Multiple Choice

What is the ratio of any two corresponding sides?  $$\frac{new}{old}$$  

• Scale Factor
• Corresponding Sides
• Similar Figures

​-If you know two angles, then you can find the third.

​-While all angles are congruent, we only state AA~

​Complete your notes by writing down the completed examples

Multiple Choice

The Angle-Angle Similarity (AA ~) Theorem states if two angles of one triangle are _______________ to two angles of another triangle, then the triangles are ____________________.

• adjacent; equal

• complementary; scalene

• congruent; similar

• supplementary; isosceles

Multiple Choice

The triangles are similar by...

• SAS
• AA
• ASA
• SSS

Multiple Choice

Are the triangles similar?

• Yes
• No

​Complete your notes by writing down the completed examples

Multiple Choice

The Side-Side-Side Similarity (SSS ~) Theorem states if the corresponding sides of two triangles are _____________________, then the triangles are _________________.

• proportional (same ratio); similar

• similar, proportional

• congruent; congruent

• equal; equilateral

Multiple Choice

The triangles are similar by...

• SAS
• AA
• ASA
• SSS

​Complete your notes by writing down the completed examples

Multiple Choice

The Side-Angle-Side Similarity (SAS ~) Theorem states that if two sides of one triangle are ________________ to two sides of another triangle and their _________________ angles are congruent, then the triangles are similar.

• adjacent; intersect

• complementary; form

• adjacent; create

• proportional (same ratio); included

Multiple Choice

The triangles are similar by...

• SAS
• AAS
• ASA
• SSS

SSS & SAS can be used to determine if triangles are similar or congruent

​

If side lengths are proportional (same ratio) = similar

​

If side lengths are the same = congruent

Special Note

Multiple Choice

What is triangular similarity

• when two triangles have three congruent sides.

• when all sides of two triangles are congruent.

• when the ratio of each side length and the angle measures are all the same.

• when the sides of two triangles are the same length and the measure of each angle is the same.

Multiple Choice

Give the reason for similarity

• AA

• SAS

• SSS

• Not similar

Multiple Choice

Are the triangles similar? If so, what similarity shortcut is used? Show all work.

• Similar.  SSS
• Similar.  SAS
• Similar.  AA
• Not Similar.

Multiple Choice

If the triangles are similar, state how.

• SSS
• SAS
• AA
• Not similar.

Open Ended

Essential Question: What information would you use to prioritize two triangles to determine if they are similar?

Multiple Choice

Do you think these triangles are similar? 

• AA
• SAS
• SSS
• Not Similar

Multiple Choice

Determine if the triangles are similar. If they are, identify the triangle similarity theorem(s) that prove(s) the similarity.

• AA ~ Theorem

• SAS ~ Theorem

• SSS ~ Theorem

• Not similar

Multiple Choice

Which triangle is not similar to any of the others?

• A
  

• B

• C

• D