1. Warm-up Say hello to your new neighbors Talk about:
What was your favorite class last semester?
What school related thing are you most excited about this semester?

2. SIMILAR
TRIANGLES

3. Similar triangles are triangles that have the same shape but not necessarily the same size.D F E
ABC  DEF
When we say that triangles are similar there are several repercussions that come from it.
A  D AB DE BC EF AC DF
= =
B  E
C  F

4. There are three special combinations that we can use to prove similarity of triangles.
1. SSS Similarity Theorem
 3 pairs of proportional sides
2. SAS Similarity Theorem
 2 pairs of proportional sides and congruent angles between them
3. AA Similarity Theorem
 2 pairs of congruent angles

5. ABC  DFE E F D 1. SSS Similarity Theorem
 3 pairs of proportional sides
9.6
10.4 A B C 5 13 12 4
ABC  DFE

6. GHI  LKJ mH = mK 2. SAS Similarity Theorem
 2 pairs of proportional sides and congruent angles between them L J K
7.5 G H I 5
70
70 7
10.5
mH = mK
GHI  LKJ

7. MNO  QRP mN = mR mO = mP 3. AA Similarity Theorem
 2 pairs of congruent angles Q P R M N O
70
50
50
70
mN = mR
MNO  QRP
mO = mP

8. TSU  XZY mT = mX mS = mZ
It is possible for two triangles to be similar when they have 2 pairs of angles given but only one of those given pairs are congruent. S T U X Y Z
34
34
34
34
59
59
mT = mX
87
59
mS = mZ
mS = 180- (34 + 87)
TSU  XZY
mS = 180- 121
mS = 59

9. Similar shapes practice
Please find a whiteboard and marker for you and your table partner

10. Congruent figures have the same _______ & _______
Vocabulary
Congruent figures have the same _______ & _______
Their corresponding parts (matching _______ and _________ ) are _________________.
size
shape
sides
angles
congruent

11. Their corresponding parts are congruent, meaning:
Congruent Figures
Their corresponding parts are congruent, meaning:
Matching _______have the same ________
sides
length
angles
degree measure

12. ∠E ≅ ∠S 𝑬𝑫 ≅ 𝑺𝑹 𝑬𝑭 ≅ 𝑺𝑻 ∠D ≅ ∠R 𝑫𝑭 ≅ 𝑹𝑻 ∠F ≅ ∠T ∆EDF ≅ ∆SRT vertices
Example 1: Naming Congruent Parts of Congruent Figures
Angles: Sides:
∠E ≅ ∠S
𝑬𝑫 ≅ 𝑺𝑹
∠D ≅ ∠R
𝑬𝑭 ≅ 𝑺𝑻
∠F ≅ ∠T
𝑫𝑭 ≅ 𝑹𝑻
∆EDF ≅ ∆SRT
Triangle Congruence Statement: _________________
vertices
 Must list corresponding ___________ in the same order

13. 𝑯𝑰 ≅ 𝑳𝑴 ∠H ≅ ∠L 𝑰𝑱 ≅ 𝑴𝑵 ∠I ≅ ∠M 𝑱𝑲 ≅ 𝑵𝑶 ∠J ≅ ∠N 𝑯𝑲 ≅ 𝑳𝑶 ∠K ≅ ∠O
Example 2: Naming Congruent Parts of Congruent Figures from a Congruence Statement
If HIJK≅LMNO, list the congruent corresponding parts.
Angles: Sides:
𝑯𝑰 ≅ 𝑳𝑴
∠H ≅ ∠L
𝑰𝑱 ≅ 𝑴𝑵
∠I ≅ ∠M
𝑱𝑲 ≅ 𝑵𝑶
∠J ≅ ∠N
∠K ≅ ∠O
𝑯𝑲 ≅ 𝑳𝑶

14. LM = GH 8 = 2x – 3 11 = 2x ∠N ≅ ∠E 72 = 7y + 9 x = 5.5 63 = 7y 9 = y
Example 3: Using Congruent Figures to Solve for Missing Values
LM = GH
8 = 2x – 3
11 = 2x
∠N ≅ ∠E
72 = 7y + 9
x = 5.5
63 = 7y
9 = y

15. ∠Y ≅ ∠S 4a – 4 = 48 4a = 52 a = 13 Example 4:
Given that ∆XYZ ≅ ∆RST, find the value of a.
∠Y ≅ ∠S
4a – 4 = 48
4a = 52
a = 13

16. 1. Write a triangle congruence statement for the two triangles below:
FGH
JKH
Δ_______ ≅ Δ_______

17. 2. If you are given that ∆AUS ≅ ∆KAP, name the three pairs of congruent sides.
𝑨𝑼 ≅ 𝑲𝑨
𝑼𝑺 ≅ 𝑨𝑷
𝑨𝑺 ≅ 𝑲𝑷

18. Third Angles Theorem
If _____ _______ of one triangle are __________ to two angles of ________ triangle, then the ______
_______ are _________.
two
angles
congruent
third
another
angles
congruent

19. ∠M ≅ ∠T m∠M = m∠T 180 – (52 + 36) 180 - 88 = 92⁰ 92⁰ = m∠T
Example 4: Using the Third Angles Theorem
∠M ≅ ∠T
m∠M = m∠T
180 – ( )
= 92⁰
92⁰ = m∠T

20. Example 6: Applying the Third Angles Theorem
Find the value of x.
x = 15

21. homework
Finish similar triangles hand-out and complete congruent shapes handout.