Triangle Similarity

Triangle Similarity:

AA, SSS, and SAS

Similar

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

​

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

​

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.

​

(but not necessarily identical)​

​

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.

​

​

​

Similarity Postulate 2: SSS

EXAMPLE!

​​

​ Each set of matching sides has the same proportion!

​

2/1 from left to right

1/2 from right to left​​

​

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:

​

*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!​​

​

Similarity Postulate 3: SAS

EXAMPLE!

​​

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

​

50=50 (identical angle)

​

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

​

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

Practice Time

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 Select

$$\Delta ASK$$ and $$\Delta ELK$$ are shown. Select all of the statements that are true.

• $$\Delta ASK\sim\Delta ELK$$ by Side-Angle-Side Similarity

• $$\Delta ASK\sim\Delta ELK$$ by Side-Side-Side Similarity

• $$\angle SKA\cong\angle LKE$$ by the Reflexive Property of Equality

• $$\angle SKA\cong\angle LKE$$ by the Vertical Angles Theorem

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 Select

$$\Delta ASK$$ and $$\Delta ELK$$ are shown. Select all of the statements that are true.

• $$\frac{AK}{EK}$$ = $$\frac{4.47}{8.94}$$

• $$\frac{SK}{LK}$$ = $$\frac{3.16}{6.32}$$

• $$\frac{AK}{EK}$$ = $$\frac{SK}{LK}$$ by the Segment Addition Postulate

• $$\frac{AK}{EK}$$ = $$\frac{SK}{LK}$$ by the Substitution Property

Multiple Choice

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

• Congruent
• Vertical
• Similar
• Complementary 

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 Select

Which statements guarantee that $$\Delta QRS\ \sim\ \Delta XYZ$$ ? Select all that apply.

• $$\Delta QRS$$ and $$\Delta XYZ$$ are equilateral.

• m∠Q = 39, m∠R = 56, m∠X = 39, m∠Z = 95

• $$\Delta XYZ$$ is a right isosceles triangle and $$m\angle Q$$ + $$m\angle R$$ = 90 $$\degree$$

• m∠R = 107, m∠S = 25, m∠X = 48 m∠Y = 107

• m∠Q + m∠S = 138 and m∠Y + m∠Z = 116

Poll

After learning this topic, I feel....

• Excited or Happy 😀

• Overwhelmed or Confused 😵

• Sad or Disappointed 😭

• Angry or Frustrated 😡

• Meh (Not Great, Not Bad) 😐